Question

Express the complex number in trigonometric form.

-3i

Answer 1

The formula to convert x+iy into r cos theta + i r sin theta is :

r = \(\sqrt{x^2+y^2}\)
\(\theta = \tan^{-1}(\dfrac{y}{x})\)

Answer 2

so, in your case,
-3i = \(\large 0-3i\)

x= 0, y = -3
plug these in the formula.

Answer 3

so r=3
i tried the 2nd formula but i got an error on my calculator

Answer 4

right, thats because tan 90 is infinity which the calculator does not support displaying.

use the fact that tan inverse (negative number/ 0) = - 90

so theta = -90

Answer 5

ok so now what

Answer 6

r and theta define your trigonometric form, r angle theta

-3i = 3 angle -90
thats it!

Answer 7

but my choices are different compared to your answer.

A) 3(cos 180° + i sin 180°)
B) 3(cos 270° + i sin 270°)
C) 3(cos 90° + i sin 90°)
D) 3(cos 0° + i sin 0°)

Answer 8

ok, so you're clear with r being 3, right ?

Answer 9

yup

Answer 10

now we need -i part,
which means cos value should be 0
cos is 0 when angle is 90 or 270

Answer 11

and since we need sin part as -1
we know sin 270 = -1

Answer 12

so, finally,
3(cos 270° + i sin 270°)

Answer 13

oh i get, thank you so much!

Answer 14

welcome ^_^