 8.4.Problem 1: Find the four fourth roots of z 81(cos 30 i sin 30). T
 8.4.a: How many nth roots does a complex number have?
 8.4.1: Every complex number has ___ distinct nth roots.
 8.4.Problem 2:
 8.4.b: How many degrees are there between the arguments of the four fourth...
 8.4.2: To find the principle nth root of a complex number, find the nth ro...
 8.4.Problem 3:
 8.4.c: How many nonreal complex solutions are there to the equation x 3 1 0?
 8.4.3: The 5th roots of a complex number would have arguments that differ ...
 8.4.d:
 8.4.4: When graphed, all of the nth roots of a complex number will be even...
 8.4.5: 4(cos 30 i sin 30)
 8.4.6: 16(cos 30 i sin 30)
 8.4.7: 25(cos 210 i sin 210)
 8.4.8: 9(cos 310 i sin 310)
 8.4.9: 49 cis 1
 8.4.10: 81 cis
 8.4.11: 2 2i3 12
 8.4.12: 2 2i3 13
 8.4.13: 4i
 8.4.14: 4i
 8.4.15: 25
 8.4.16: 25
 8.4.17: i3 18
 8.4.18: 1 i3
 8.4.19: 8(cos 210 i sin 210) 2
 8.4.20: 27(cos 303 i sin 303)
 8.4.21: 434i 22
 8.4.22: 43 4i 2
 8.4.23: 27
 8.4.24: 8
 8.4.25: 64i
 8.4.26: 64i
 8.4.27: x3 8 0 2
 8.4.28: x3 27 0
 8.4.29: x4 81 0 3
 8.4.30: x4 16 0
 8.4.31: Find the 4 fourth roots of z 16(cos 2 3 i sin 2 3 ). Write each roo...
 8.4.32: Find the 4 fourth roots of z cos 4 3 i sin 4 3 . Leave your answers...
 8.4.33: Find the 5 fifth roots of z 105 cis 15. Write each root in trigonom...
 8.4.34: Find the 5 fifth roots of z 1010
 8.4.35: Find the 6 sixth roots of z 1. Leave your answers in trigonometric ...
 8.4.36: Find the 6 sixth roots of z 1. Leave your answers in trigonometric ...
 8.4.37: x4 2x2 4 0 3
 8.4.38: x4 2x2 4 0 3
 8.4.39: x4 2x2 2 0 40
 8.4.40: x4 2x2 2 0
 8.4.41: y 2 sin (3x), 0 x 2
 8.4.42: y 2 cos (3x), 0 x 2 G
 8.4.43: y cos 2x 44
 8.4.44: y 3 sin x
 8.4.45: A 56.2, b 2.65 cm, and c 3.84 cm 46
 8.4.46: B 21.8, a 44.4 cm, and c 22.2 cm 47
 8.4.47: a 2.3 ft, b 3.4 ft, and c 4.5 ft 4
 8.4.48: a 5.4 ft, b 4.3 ft, and c 3.2 ft
 8.4.49: Recall from the introduction to Section 8.2 that Jerome Cardans sol...
 8.4.50: Find the two square roots of 36i. a. 323i2, 32 3i2 b. 32 3i2, 323i2...
 8.4.51: Which of the following is one of the fifth roots of 32 cis 40? a. 2...
 8.4.52: Which graph could represent the fourth roots of some complex number...
 8.4.53: Solve x3 64 0. Which of the following is a solution? a. 2 2i 3 b. 2...
Solutions for Chapter 8.4: Roots of a Complex Number
Full solutions for Trigonometry  7th Edition
ISBN: 9781111826857
Solutions for Chapter 8.4: Roots of a Complex Number
Get Full SolutionsChapter 8.4: Roots of a Complex Number includes 60 full stepbystep solutions. Since 60 problems in chapter 8.4: Roots of a Complex Number have been answered, more than 24935 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Trigonometry was written by and is associated to the ISBN: 9781111826857. This textbook survival guide was created for the textbook: Trigonometry, edition: 7.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

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.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

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

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

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.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.