Question

w=2sqrt2(cos(225)+isin(225))
what is w^4?

Answer 1

Are you familiar with De Moivre's Theorem?

Answer 2

a little

Answer 3

@jim_thompson5910 i've got 2sqrt2 (cos(450)+isin(450)) so far

Answer 4

2sqrt2^4*

Answer 5

so what is \(\Large \left(2\sqrt{2}\right)^4\) equal to?

Answer 6

64

Answer 7

would theta be 900 instead of 450?

Answer 8

how are you getting 900?

Answer 9

4 x 225

Answer 10

oh right, I was looking at the wrong part

Answer 11

yes, you'll have 64*( cos(900) + i*sin(900) )

Answer 12

then you'll need to find the angle coterminal to 900 degrees such that this angle is in the interval [0, 360)

Answer 13

i got 180?

Answer 14

@jim_thompson5910 is the answer \[-2\sqrt{2}\] ?

Answer 15

64*( cos(900) + i*sin(900) ) = 64*( cos(180) + i*sin(180) )

64*( cos(900) + i*sin(900) ) = 64*( -1 + 0 )

64*( cos(900) + i*sin(900) ) = -64

Answer 16

so that means

\[\Large w^4 = -64\]

where

\[\Large w = 2\sqrt{2}(\cos(225^{\circ})+i\sin(225^{\circ}))\]

Answer 17

I'm not sure how you got that result

Answer 18

thank you