Convert -2i to it's trigonometric form

Question

Convert equation to trigonometric form

Answer 1

z = -2i

 

In polar form:

 

z = r(cosθ + i·sinθ)

 

If you represent it on a graph (Argand Diagram), it's easy to see that

• r = 2
• θ = 270°

So we have z = 2·(cos(270°) + i·sin(270°))

Answer 2

Recall that

 

i = e^iπ/2 = cos(π/2) + i sin(π/2) = 0 + 1i

 

Then

 

-2i = -2cos(π/2) - i2sin(π/2)