# How do you write 3(cos(90)+isin(90)) in rectangular form?

Feb 4, 2015

I think you are working in degrees here, so you simply multiply $3$ times whatever you have inside your brackets.

In this case:

cos(90°)=0
sin(90°)=1

So you get:

z=3(cos(90°)+isin(90°))=3*(0+i*1)=3i

Your number is a pure imaginary.

You can also see this by plotting your complex number $z$ on the complex plane:

hope it helps