How is a complex number represented in polar form?

A complex number is represented in polar form as r(cosθ + i sinθ).

In polar form, a complex number is represented by its magnitude (r) and argument (θ). The magnitude is the distance from the origin to the point representing the complex number in the complex plane, and the argument is the angle between the positive real axis and the line connecting the origin to the point representing the complex number.

To convert a complex number from rectangular form (a + bi) to polar form, we can use the following formulas:

r = √(a^2 + b^2)
θ = tan^-1(b/a)

To convert a complex number from polar form to rectangular form, we can use the following formulas:

a = r cosθ
b = r sinθ

For example, let's convert the complex number 3 + 4i to polar form. We have:

r = √(3^2 + 4^2) = 5
θ = tan^-1(4/3) ≈ 0.93 radians

Therefore, the complex number 3 + 4i can be represented in polar form as 5(cos0.93 + i sin0.93).