How do you find the power $(-2+2i)^3$ and express the result in rectangular form?

Question

6300 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-30T19:49:46

$= 16 ( 1 + i)$

We use polar complex first t o simplify down

let $R e^(i theta) = -2 + 2i$

$= 2 sqrt 2 (-1/sqrt 2 + i /sqrt 2)$

We will find -ve value for $cos theta$ and +ve value for $sin theta$ in Q2 of the Argand diagram.

$implies theta = (3 pi) /4$

$implies R e^(i theta) = 2 sqrt 2 e^(i (3 pi) /4)$

$implies (R e^(i theta))^3 = (2 sqrt 2)^3 e^(i (3*3 pi) /4)$

$= 16 sqrt 2e^(i (pi) /4)$

$= 16 ( 1 + i)$

clearly you could also use a binomial expansion :)

How do you find the power (-2+2i)^3(-2+2i)^3 and express the result in rectangular form?