Question

Express the complex number in trigonometric form.

-2i

2(cos 180° + i sin 180°)
2(cos 90° + i sin 90°)
2(cos 270° + i sin 270°)
2(cos 0° + i sin 0°)

Answer 1

you can write a complex number as Z
let Z=0-2i
so Z=-2i

you know that the complex number Z can be written
Z=r(cos(x)+isin(x))

Answer 2

r is the magnitude of your complex number

Answer 3

for example if I have a complex number
3-2i

r would be the magnitude so
\[r=\sqrt{3^{2}+(-2)^{2}}\]

Answer 4

you can work out the angle by doing
\[\theta= \tan^{-1}(\frac{ b }{ a})\]

Answer 5

where b is the complex number coefficient and a is the real number

Answer 6

similarly you could figure this out by using a graph

Answer 7

hint: