 55.1: Tim said that the binomial x2 1 16 can be written as x2 2 16i 2 and...
 55.2: Joshua said that the product of a complex number and its conjugate ...
 55.3: In 317, find each sum or difference of the complex numbers in a + b...
 55.4: In 317, find each sum or difference of the complex numbers in a + b...
 55.5: In 317, find each sum or difference of the complex numbers in a + b...
 55.6: In 317, find each sum or difference of the complex numbers in a + b...
 55.7: In 317, find each sum or difference of the complex numbers in a + b...
 55.8: In 317, find each sum or difference of the complex numbers in a + b...
 55.9: In 317, find each sum or difference of the complex numbers in a + b...
 55.10: In 317, find each sum or difference of the complex numbers in a + b...
 55.11: In 317, find each sum or difference of the complex numbers in a + b...
 55.12: In 317, find each sum or difference of the complex numbers in a + b...
 55.13: In 317, find each sum or difference of the complex numbers in a + b...
 55.14: In 317, find each sum or difference of the complex numbers in a + b...
 55.15: In 317, find each sum or difference of the complex numbers in a + b...
 55.16: In 317, find each sum or difference of the complex numbers in a + b...
 55.17: In 317, find each sum or difference of the complex numbers in a + b...
 55.18: In 1825, write the complex conjugate of each number. 3 1 4i
 55.19: In 1825, write the complex conjugate of each number. 2 2 5i
 55.20: In 1825, write the complex conjugate of each number. 28 1 i
 55.21: In 1825, write the complex conjugate of each number. 26 2 9i
 55.22: In 1825, write the complex conjugate of each number. 1 2 2 3i
 55.23: In 1825, write the complex conjugate of each number. 4 1 i 1 3i
 55.24: In 1825, write the complex conjugate of each number. 5 3 2 2 3
 55.25: In 1825, write the complex conjugate of each number. p 1 2i
 55.26: In 2637, find each product. (1 1 5i)(1 1 2i)
 55.27: In 2637, find each product. (3 1 2i)(3 1 3i)
 55.28: In 2637, find each product. (2 2 3i)2
 55.29: In 2637, find each product. (4 2 5i)(3 2 2i)
 55.30: In 2637, find each product. (7 1 i)(2 1 3i)
 55.31: In 2637, find each product. (22 2 i)(1 1 2i)
 55.32: In 2637, find each product. (24 2 i)(24 1 i)
 55.33: In 2637, find each product. (212 2 2i)(12 2 2i)
 55.34: In 2637, find each product. (5 2 3i)(5 1 3i)
 55.35: In 2637, find each product. (3 2 i)
 55.36: In 2637, find each product. (4 1 2i)
 55.37: In 2637, find each product. (4 1 4i)
 55.38: In 3845, find the multiplicative inverse of each of the following i...
 55.39: In 3845, find the multiplicative inverse of each of the following i...
 55.40: In 3845, find the multiplicative inverse of each of the following i...
 55.41: In 3845, find the multiplicative inverse of each of the following i...
 55.42: In 3845, find the multiplicative inverse of each of the following i...
 55.43: In 3845, find the multiplicative inverse of each of the following i...
 55.44: In 3845, find the multiplicative inverse of each of the following i...
 55.45: In 3845, find the multiplicative inverse of each of the following i...
 55.46: In 4660, write each quotient in a + bi form. (8 1 4i) 4 (1 1 i)
 55.47: In 4660, write each quotient in a + bi form. (2 1 4i) 4 (1 2 i)
 55.48: In 4660, write each quotient in a + bi form. (10 1 5i) 4 (1 1 2i)
 55.49: In 4660, write each quotient in a + bi form. (5 2 15i) 4 (3 2 i)
 55.50: In 4660, write each quotient in a + bi form.
 55.51: In 4660, write each quotient in a + bi form.
 55.52: In 4660, write each quotient in a + bi form.
 55.53: In 4660, write each quotient in a + bi form.
 55.54: In 4660, write each quotient in a + bi form.
 55.55: In 4660, write each quotient in a + bi form.
 55.56: In 4660, write each quotient in a + bi form.
 55.57: In 4660, write each quotient in a + bi form.
 55.58: In 4660, write each quotient in a + bi form.
 55.59: In 4660, write each quotient in a + bi form.
 55.60: In 4660, write each quotient in a + bi form.
 55.61: Impedance is the resistance to the flow of current in an electric c...
 55.62: Find the current that will flow when V 5 1.6 2 0.3i volts and Z 5 1...
Solutions for Chapter 55: Operations With Complex Numbers
Full solutions for Amsco's Algebra 2 and Trigonometry  1st Edition
ISBN: 9781567657029
Solutions for Chapter 55: Operations With Complex Numbers
Get Full SolutionsChapter 55: Operations With Complex Numbers includes 62 full stepbystep solutions. Since 62 problems in chapter 55: Operations With Complex Numbers have been answered, more than 28366 students have viewed full stepbystep solutions from this chapter. Amsco's Algebra 2 and Trigonometry was written by and is associated to the ISBN: 9781567657029. This textbook survival guide was created for the textbook: Amsco's Algebra 2 and Trigonometry, edition: 1. This expansive textbook survival guide covers the following chapters and their solutions.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Iterative method.
A sequence of steps intended to approach the desired solution.

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)ยท(b  Ax) = o.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Solvable system Ax = b.
The right side b is in the column space of A.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

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).