Polar form of complex numbers - Practice Questions & MCQ

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

Let $z=x+i y$ be a complex number,

And we know that 

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

And let arg(z) = θ 

From the figure, $x=|z| \cos (\theta)=r \cos (\theta)$
and $y=|z| \sin (\theta)=r \sin (\theta)$
So, $z=x+i y=r \cos (\theta)+i . r \sin (\theta)=r(\cos (\theta)+i . \sin (\theta))$
This form is called polar form with $r=$ principal value of $\arg (z)$ and $r=|z| . \mid$

For general values of the argument

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