X 8335 Question Help Use a calculator to perform the indica

X 8.3.35 Question Help * Use a calculator to perform the indicated operation. Give the answer in rectangular form (3cis)\' 4z 4x Type your answer in the form a+bi. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer.

Solution

from calculator (3cis(4_/5))² =2.7812 +(-8.5595)i , where a=2.7812, b=-8.5595

or simply (3cis(4_/5))² =2.7812 -8.5595i

(3cis(4_/5))² =3²(cis(4_/5))²

=>(3cis(4_/5))² =9(cis(2*4_/5))

=>(3cis(4_/5))² =9(cis(8_/5))

=>(3cis(4_/5))² =9(cos(8_/5)+ i sin(8_/5))

=>(3cis(4_/5))² =9*(0.309012994374947424+ i(-0.95105651629515357211643933337938))

=>(3cis(4_/5))² =(9*0.309012994374947424)+ i(-9*0.95105651629515357211643933337938)

=>(3cis(4_/5))² =(2.7811529493745268169206407546454)+ i(-8.5595086466563821490479540004145)

=>(3cis(4_/5))² =2.7812 -8.5595i