Question

Complex numbers! (1+i)^14?

Answer 1

job one is to write it in trig form (polar form)
do you know how to do that?

Answer 2

i.e. write it as \[r\left(\cos(\theta)+i\sin(\theta)\right)\]

Answer 3

sqrt 2 (cos pi/4 + i sin pi/4)?

Answer 4

yes!

Answer 5

@Satellite73 Thank you! Just a massive brain fart.

Answer 6

so you have only two easy steps now
\[\sqrt{2}^{14}\] for the absolute value (modulus) and \[14\times \frac{\pi}{4}\]for the angle

Answer 7

is it clear what \[\sqrt{2}^{14}\] is ?

Answer 8

without a calculator i mean
with a calculator it is easy

Answer 9

Yep! Just that one step that really bugged me. Thanks! @Satellite73

Answer 10

yw