Question

Let z = re
jθ
expressed in polar form, determine the magnitude and angle for the

following functions of z:

Answer 1

Answer:

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Answer 2

The Complex number in polar form is z = $re^{i(theta)}$

The complex number in polar form represents a circle on the complex plane with the centre at the origin. The radius of the circle is the magnitude of the complex number.

Converting the given complex number into the cartesian form we have,

z = rcosθ + i(rsinθ)

We are assuming that θ lies between 0 degrees to 90 degrees.

From here, it is clear that the magnitude of the given complex number is r.

Let the angle be A,

TanA = sinθ/cosθ

TanA = tanθ

A = $tan^{-1}tan$θ

Condition on the angle A is that o° < A < 90°.

A = θ

Therefore, the magnitude of the given function is r, and the angle is θ.