 7.7.1: Simplify. See Example 1.281
 7.7.2: Simplify. See Example 1.249
 7.7.3: Simplify. See Example 1.27
 7.7.4: Simplify. See Example 1.23
 7.7.5: Simplify. See Example 1.  216
 7.7.6: Simplify. See Example 1. 24
 7.7.7: Simplify. See Example 1.264
 7.7.8: Simplify. See Example 1.2100
 7.7.9: Write in terms of i. See Example 1.224
 7.7.10: Write in terms of i. See Example 1.232
 7.7.11: Write in terms of i. See Example 1. 236
 7.7.12: Write in terms of i. See Example 1. 2121
 7.7.13: Write in terms of i. See Example 1.8263
 7.7.14: Write in terms of i. See Example 1.4220
 7.7.15: Write in terms of i. See Example 1. 254
 7.7.16: Write in terms of i. See Example 1.263
 7.7.17: Multiply or divide. See Example 2.22 # 27
 7.7.18: Multiply or divide. See Example 2.211 # 23
 7.7.19: Multiply or divide. See Example 2.25 # 210
 7.7.20: Multiply or divide. See Example 2.22 # 26
 7.7.21: Multiply or divide. See Example 2.216 # 21
 7.7.22: Multiply or divide. See Example 2.23 # 227
 7.7.23: Multiply or divide. See Example 2.2923
 7.7.24: Multiply or divide. See Example 2.249210
 7.7.25: Multiply or divide. See Example 2.280210
 7.7.26: Multiply or divide. See Example 2.24028
 7.7.27: Add or subtract. Write the sum or difference in the form a + bi. Se...
 7.7.28: Add or subtract. Write the sum or difference in the form a + bi. Se...
 7.7.29: Add or subtract. Write the sum or difference in the form a + bi. Se...
 7.7.30: Add or subtract. Write the sum or difference in the form a + bi. Se...
 7.7.31: Add or subtract. Write the sum or difference in the form a + bi. Se...
 7.7.32: Add or subtract. Write the sum or difference in the form a + bi. Se...
 7.7.33: Multiply. Write the product in the form a + bi. See Example 4.10i ...
 7.7.34: Multiply. Write the product in the form a + bi. See Example 4.2i #...
 7.7.35: Multiply. Write the product in the form a + bi. See Example 4.6i12 ...
 7.7.36: Multiply. Write the product in the form a + bi. See Example 4.5i14 ...
 7.7.37: Multiply. Write the product in the form a + bi. See Example 4. 23 +...
 7.7.38: Multiply. Write the product in the form a + bi. See Example 4.1 25 ...
 7.7.39: Multiply. Write the product in the form a + bi. See Example 4.14  ...
 7.7.40: Multiply. Write the product in the form a + bi. See Example 4.16  ...
 7.7.41: Write each quotient in the form a + bi. See Example 5.4i
 7.7.42: Write each quotient in the form a + bi. See Example 5.56i
 7.7.43: Write each quotient in the form a + bi. See Example 5.74 + 3i
 7.7.44: Write each quotient in the form a + bi. See Example 5.91  2i
 7.7.45: Write each quotient in the form a + bi. See Example 5.3 + 5i1 + i
 7.7.46: Write each quotient in the form a + bi. See Example 5.6 + 2i4  3
 7.7.47: Write each quotient in the form a + bi. See Example 5.5  i3  2i
 7.7.48: Write each quotient in the form a + bi. See Example 5.6  i2 + i
 7.7.49: Perform each indicated operation. Write the result in the form a + ...
 7.7.50: Perform each indicated operation. Write the result in the form a + ...
 7.7.51: Perform each indicated operation. Write the result in the form a + ...
 7.7.52: Perform each indicated operation. Write the result in the form a + ...
 7.7.53: Perform each indicated operation. Write the result in the form a + ...
 7.7.54: Perform each indicated operation. Write the result in the form a + ...
 7.7.55: Perform each indicated operation. Write the result in the form a + ...
 7.7.56: Perform each indicated operation. Write the result in the form a + ...
 7.7.57: Perform each indicated operation. Write the result in the form a + ...
 7.7.58: Perform each indicated operation. Write the result in the form a + ...
 7.7.59: Perform each indicated operation. Write the result in the form a + ...
 7.7.60: Perform each indicated operation. Write the result in the form a + ...
 7.7.61: Perform each indicated operation. Write the result in the form a + ...
 7.7.62: Perform each indicated operation. Write the result in the form a + ...
 7.7.63: Perform each indicated operation. Write the result in the form a + ...
 7.7.64: Perform each indicated operation. Write the result in the form a + ...
 7.7.65: Perform each indicated operation. Write the result in the form a + ...
 7.7.66: Perform each indicated operation. Write the result in the form a + ...
 7.7.67: Perform each indicated operation. Write the result in the form a + ...
 7.7.68: Perform each indicated operation. Write the result in the form a + ...
 7.7.69: Perform each indicated operation. Write the result in the form a + ...
 7.7.70: Perform each indicated operation. Write the result in the form a + ...
 7.7.71: Perform each indicated operation. Write the result in the form a + ...
 7.7.72: Perform each indicated operation. Write the result in the form a + ...
 7.7.73: Perform each indicated operation. Write the result in the form a + ...
 7.7.74: Perform each indicated operation. Write the result in the form a + ...
 7.7.75: Perform each indicated operation. Write the result in the form a + ...
 7.7.76: Perform each indicated operation. Write the result in the form a + ...
 7.7.77: Perform each indicated operation. Write the result in the form a + ...
 7.7.78: Perform each indicated operation. Write the result in the form a + ...
 7.7.79: Perform each indicated operation. Write the result in the form a + ...
 7.7.80: Perform each indicated operation. Write the result in the form a + ...
 7.7.81: Find each power of i. See Example 6.i 8
 7.7.82: Find each power of i. See Example 6.i 10
 7.7.83: Find each power of i. See Example 6.i 21
 7.7.84: Find each power of i. See Example 6.i 15
 7.7.85: Find each power of i. See Example 6.i 11
 7.7.86: Find each power of i. See Example 6.i 40
 7.7.87: Find each power of i. See Example 6.i 6
 7.7.88: Find each power of i. See Example 6.i 9
 7.7.89: Find each power of i. See Example 6.12i26
 7.7.90: Find each power of i. See Example 6.15i24
 7.7.91: Find each power of i. See Example 6.1 3i25
 7.7.92: Find each power of i. See Example 6. 1 2i27
 7.7.93: Recall that the sum of the measures of the angles of a triangle is ...
 7.7.94: Recall that the sum of the measures of the angles of a triangle is ...
 7.7.95: Use synthetic division to divide the following. See Section 6.4.1x3...
 7.7.96: Use synthetic division to divide the following. See Section 6.4.15x...
 7.7.97: Thirty people were recently polled about the average monthly balanc...
 7.7.98: Thirty people were recently polled about the average monthly balanc...
 7.7.99: Thirty people were recently polled about the average monthly balanc...
 7.7.100: Thirty people were recently polled about the average monthly balanc...
 7.7.101: Thirty people were recently polled about the average monthly balanc...
 7.7.102: Thirty people were recently polled about the average monthly balanc...
 7.7.103: Write in the form a + bi.i 3  i 4
 7.7.104: Write in the form a + bi.i 8  i 7
 7.7.105: Write in the form a + bi.i 6 + i 8
 7.7.106: Write in the form a + bi. i 4 + i 12
 7.7.107: Write in the form a + bi.2 + 29
 7.7.108: Write in the form a + bi.5  216
 7.7.109: Write in the form a + bi.6 + 2183
 7.7.110: Write in the form a + bi.4  282
 7.7.111: Write in the form a + bi.5  27510
 7.7.112: Write in the form a + bi.7 + 29814
 7.7.113: Describe how to find the conjugate of a complex number
 7.7.114: Explain why the product of a complex number and its complex conjuga...
 7.7.115: Simplify.18  232  12 + 2122
 7.7.116: 18  242  12 + 2162
 7.7.117: Determine whether 2i is a solution of x2 + 4 = 0
 7.7.118: Determine whether 1 + i is a solution of x2 + 2x = 2.
Solutions for Chapter 7.7: Complex Numbers
Full solutions for Intermediate Algebra  6th Edition
ISBN: 9780321785046
Solutions for Chapter 7.7: Complex Numbers
Get Full SolutionsIntermediate Algebra was written by and is associated to the ISBN: 9780321785046. This textbook survival guide was created for the textbook: Intermediate Algebra, edition: 6. Since 118 problems in chapter 7.7: Complex Numbers have been answered, more than 28730 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7.7: Complex Numbers includes 118 full stepbystep solutions.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).