Question

In the complex plane, the rectangular coordinates (x, y) represent a complex number. Which statement explains why polar coordinates (r, θ) represent the same complex number?

r is equivalent to StartRoot x squared + y squared EndRoot and θ is equivalent to Inverse tangent of (StartFraction x Over y EndFraction).
r is equivalent to StartRoot x squared + y squared EndRoot and θ is equivalent to Inverse tangent of (StartFraction x Over y EndFraction).
r is equivalent to StartRoot x squared + y squared EndRoot and θ is equivalent to Inverse tangent of (StartFraction x Over y EndFraction).
r is equivalent to StartRoot x squared + y squared EndRoot and θ is equivalent to Inverse tangent of (StartFraction x Over y EndFraction)

Answer 1

The correct option is;

r = √(x² + y²)

θ = tan⁻¹(y/x)

Explanation:

The rectangular coordinate of a complex number on the complex plane is given as (x, y)

Given that the complex number is represented by a point on the plane, we have;

The distance, r, of the point from the origin, (0, 0) is r = √(x² + y²)

The direction, θ, by which we rotate to be in line with the point on the complex number is given by tan⁻¹(y/x)