Polar form of complex numbers MCQ - Practice Questions & Answers

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Polar form of complex numbers

In polar form, we represent the complex number through the argument and modulus value of complex numbers.

Let z = x + iy be a complex number,

And we know that

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

And let arg(z) = θ

From the figure, x = |z| cos(θ) = r cos(θ)

and y = |z| sin(θ) = r sin(θ)

So, z = x + iy = r cos(θ) + i.r sin(θ) = r ( cos(θ) + i.sin(θ))

This form is called polar form with ? = principal value of arg(z) and r = |z|.

For general values of the argument

$\\\mathrm{z=r[\cos(2n\pi+\theta)+\mathit{i}\sin(2n\pi+\theta)]},\;\;where\;\;n\;\in Integer$

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Polar form of complex numbers - Practice Questions & MCQ

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