Learning Journal Unit 8 PDF

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Learning Journal Unit 8...

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Complete the following questions utilizing the concepts introduced in this unit. The assignment will be graded by your instructor. 1. Evaluate the cube root of your reasoning.

. Then raise them to the cube. Show the steps of

240 degree = 4pi/3 = 27 cis (4pi/3) We have, according to n-th root theorem: Z ^ 1/3 = 3 [ cos (4pi/9 + k2pi/3) + i sin (4pi/ 9 + k2pi/3) ] Let calculate its cube root: Z ^1/3 = Then we raise them to the cube: Z ^ 3 = 27 ^ 3 ( cós 4pi + I sin 4pi) = 19683 ( 1 + 0i) = 19683

2. Evaluate

.

= 3 ^ 2 [cos ( 10 pi / 6) + i sin (10pi /6) ] = 9 ( 1/2 - root3 / 2) =9/2 (1-root3) 3.29

3. Find

in polar form:

�1= 21 ���(135�) �2= 3 ���(75�) �1/�2 = �1/�2 ���(θ1− θ2) �1/z2= 21/3 ���(135�− 75�) �1/�2 = 7 ���(θ1− θ2) �1/z2 = 7���(60�) �1/z2 = 7(���(60�) + ����(60�))

�1/z2 = 7(1/2 + � 3/2) �1/z2 = 7/2 + (21/2)�...