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?

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 =

By applying tangent rule in ΔAPO,

tanθ =

tanθ =

θ =

Therefore, Option 2 will be the correct option.

step-by-step explanation:

i have done this all on a piece of paper but idk how to put it on here cuz it needs to be drawn

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step-by-step explanation: