1720 EXX C Response dep 15158991 Assignment submission For t

1720 EXX C Response dep 15158991 Assignment submission For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes you submit or change the answer Assignment scoring Your last submission is used for your score. 12. -1 points SPreCalc7 8.3.072 My Notes Ask Your Teacher Find the indicated power using De Moivre\'s Theorem Express your fully simplified answer in the form a bi. 10 Submit Answer Save Progress View Previous Question Question 12 of 24 View Next Question Home My Assignments Extension Request\' WebAssign 4.0 1997-2016 Advanced Instructional Systems, Inc. All rights reserved.

Solution

(-3_/2 -1_/2i )¹⁰

r=[(-3_/2)²+(-1_/2)²]

r =1

=+tan^-1[(1/2)_/(3/2)]

=+tan^-1[1_/3]

=+(_/6)

=(7_/6)

(-3_/2 -1_/2i )¹⁰

=(cos(7_/6) +isin(7_/6))¹⁰

=(cos(10*7_/6) +isin(10*7_/6))

=(cos(35_/3) +isin(35_/3))

=((1_/2) -i(3_/2))

so (-3_/2 -1_/2i )¹⁰=((1_/2) - (3_/2)i)