Question

Express the complex number in trigonometric form.

-2i

Answer 1

In order to use the trigonometric form, of a complex number z, find its modulus r and its argument theta,
\[z=r(\cos\theta+i\sin\theta)\]

Answer 2

For a pure negative imaginary number, you know that theta is 3pi/2. In this case, also, the modulus is easy because is 2.
So the trigonometric representation is,
\[z=2(\cos(3\pi/2)+i\sin(3\pi/2))\]

Answer 3

2(cos 270° + i sin 270°) Would be correct then?

Answer 4

Perfect.

Answer 5

Thank you sir :p @John_ES

Answer 6

You're welcome.