Question

What is the polar form of -4+5i?

Answer 1

z= r(cosθ+i sinθ) is the required polar form where, r = √41 and θ =π-
`tan^(-1) ((5)/(4) )`

Explanation:

Given,

-4+5i is a complex number.

To find the polar form.

Formula

z=x+iy

r² = mod of (x²+y²)

θ =
`tan^(-1) ((y)/(x) )`

So, the polar form will be z=r(cosθ+i sinθ)

Now,

r² =(-4)²+5² = 41

or, r = √41

θ =π-
`tan^(-1) ((5)/(4) )` [ since the point is in second quadrant]

Hence,

z= r(cosθ+i sinθ) is the required polar form where, r = √41 and θ =π-
`tan^(-1) ((5)/(4) )`