Question

Express the complex number in trigonometric form.

-2 + 2sqrt3 i

Answer 1

\[-2+2\sqrt{3}i\]

Answer 2

@jim_thompson5910 @aaronq

Answer 3

you need two numbers \(r\) and \(\theta\) in order to write this as
\[-2+3\sqrt 3 i=r\left(\cos(\theta)+i\sin(\theta)\right)\]

Answer 4

\(r\) is the easiest to find, is is
\[r=\sqrt{a^2+b^2}\] in your case \(a=-2,b=2\sqrt3\)

Answer 5

ok, lets see

Answer 6

k i will for you
let me know what you get

Answer 7

1.414

Answer 8

forget the calculator

Answer 9

just do it by hand

Answer 10

4

Answer 11

\[\sqrt{2^2+(2\sqrt3)^2}=\sqrt{4+12}=\sqrt{16}=4\] right

Answer 12

alright

Answer 13

now you need \(\theta\) which may or may not be obvious

Answer 14

you can use \(\tan(\theta)=\frac{b}{a}\)

Answer 15

or in your example
\[\tan(\theta)=-\sqrt3\]

Answer 16

ok, i'm sorry for wasting your time, i actually solved this problem already and mistakenly didn't mark it off as complete

Answer 17

the answer is
4 (cos(2pi/3) + i sin (2pi/3)

sorry again, thanks!

Answer 18

@satellite73

Answer 19

lol yw