Question 1206992
<br>
Use deMoivre's Theorem.<br>
{{{x^5-32=0}}}
{{{x^5=32}}}<br>
ANSWERS:
(1) {{{x^5=32=32cis(0)=32e^(0i)}}}; {{{x=(x^5)^(1/5)=2cis(0)=2e^(i(0))=2}}}
(2) {{{x^5=32=32cis(2pi)=32e^((2pi)i)}}}; {{{x=(x^5)^(1/5)=2cis((2pi)/5)=2e^i(2pi/5)}}}
(3) {{{x^5=32=32cis(4pi)=32e^((4pi)i)}}}; {{{x=(x^5)^(1/5)=2cis((4pi)/5)=2e^i(4pi/5)}}}
(4) {{{x^5=32=32cis(6pi)=32e^((6pi)i)}}}; {{{x=(x^5)^(1/5)=2cis((6pi)/5)=2e^i(6pi/5)}}}
(5) {{{x^5=32=32cis(8pi)=32e^((8pi)i)}}}; {{{x=(x^5)^(1/5)=2cis((8pi)/5)=2e^i(8pi/5)}}}<br>