6i write the complex number in polar form.express the argument in degrees

Question

6i write the complex number in polar form.express the argument in degrees

Answer 1

Hi Leonel,

 

The polar form of a complex number z=a+bi can be written as

z=r(cosθ+isinθ)

r represents the absolute value or modulus, and the angle θ is the argument of the complex number (i.e., the angle made with the real axis).

Then, we can write

|z| = r = sqrt(a^2 + b^2)

The complex number given is 6i so

a = 0, b = 6

|z| = r = sqrt(6^2)

= 6

On the coordinate plane, this number is on the imaginary axis and is perpendicular to the real axis. As a result, angle θ = 90 deg

then 6i is equal to 6*(cos90+isin90) in polar form.