Question

How do you write the complex number `-2i` in polar form?

Answer 1

Please see the explanation.

Explanation:

Because the real part (a) of the complex number is zero, you cannot use `theta = tan^-1(b/a)`; you must know that the angle is either `pi/2` or `3pi/2`. Because the sign of the complex part is negative, you must know that this makes the angle the latter, `3pi/2`.

`theta = 3pi/2`

You can see that the magnitude is 2.

The polar form is:

`2(cos(3pi/2)+isin(3pi/2))`

Answer 2

I hope a get it right: `2*(cos(270)+isin(270))`

Explanation:

`r=sqrt(x^2+y^2)=sqrt(4)=2`
`alpha=ctg^(-1)(0/-2)=90`
`alpha=360-90=270`

In polar:
`2*(cos(270)+isin(270))`