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?

Answer 1

Answer:

Option (2)

Step-by-step explanation:

From the picture attached,

Let the rectangular coordinates (x, y) is represented by the polar coordinates (r, θ).

By applying Pythagoras theorem in ΔPAO,

PO² = AO² + AP²

r² = x² + y²

r = $\sqrt{x^2+y^2}$

By applying tangent rule in ΔAPO,

tanθ = $\frac{AP}{OA}$

tanθ = $\frac{y}{x}$

θ = $\text{tan}^{-1}(\frac{y}{x})$

Therefore, Option 2 will be the correct option.