Question

Rewrite the rectangular form of the complex number in its equivalent polar form. Approximate all angle measures to the nearest degree.

z = 3 + 2i

Answer 1

Rectangular form of z is z = 3 + 2i

Polar form of complex number is (r ,
`\theta`).

In general if z = x + iy


`r = √(x^2 + y^2)`


`\theta = tan^(-1) (y)/(x)`

So in given complex number z = 3 + 2i

So r is

`r = √((3)^2 + (2)^2)`

`= √(9 + 4 ) = √(13)`


`\theta = tan^(-1) ( (y)/(x)) = tan^(-1) ( (2)/(3)}`

`= 33.703` degree.

So the rectangular form is
`( √(13) , 33.703` degree ).