Question

Express the following complex number in the form re^(i theta)

Answer 1

6i

Answer 2

I know I need to use r cos theta+ i sin theta

Answer 3

if you plot it, it might be self-evident

Answer 4

The book wants the mathematical description. I need to find r?

Answer 5

of course you want a theta so that cos theta =0

Answer 6

it is almost the same problem as changing (x,y) to polar coords

Answer 7

Here is whtat the book says do but I dont get it. 6i=r cos theta + i r sin theta
r=6 (why?)
inverse tan (6/0) is pi/2 so it is 6e^(I PI/2)

Answer 8

the "r" factors out
r ( cos x + i sin x)
the magnitude squared is r^2 * 1
(right?)
and square root gives r

Answer 9

i really do think drawing it first as @phi suggested will get your understanding there quickest

Answer 10

This is pchem math review I'm not really sure how to draw it just trying to make sense of this.