Argand Plane and Polar Representation

If $x+iy=cis\alpha .cis\beta ,$ then find the value of $x^2+y^2.$

Find the real and imaginary parts of the complex number $z=25\left(2+3i\right)$

Find the real and imaginary parts of the complex number $z=\sqrt{2}\left(2-i\right)$

Write the polar coordinates of the complex number $3+i3\sqrt{3}$

Write the polar coordinates of the complex number $2+i2\sqrt{3}$

Write the polar coordinate of the complex number $\sqrt{3}+i$

Given two complex numbers $Z_1=3\left(\cos \theta +i\sin \theta \right)$ and $Z_2=2\left(\cos \theta +i\sin \theta \right)$. Find $Z_1-Z_2$

Given two complex numbers $Z_1=4\left(\cos \theta +i\sin \theta \right)$ and $Z_2=7\left(\cos \theta +i\sin \theta \right)$. Find $Z_1-Z_2$

Given two complex numbers $Z_1=4\left(\cos \theta -i\sin \theta \right)$ and $Z_2=7\left(\cos \theta -i\sin \theta \right)$. Find $Z_1-Z_2$

Find $Z_1-Z_2$, given two complex in polar form $Z_1=24\left(\cos \theta +i\sin \theta \right)$ and $Z_2=27\left(\cos \theta +i\sin \theta \right)$ 

Subtract $Z_1=18\left(\cos \theta +i\sin \theta \right)$ and $Z_2=33\left(\cos \theta +i\sin \theta \right)$ 

Add $Z_1=18\left(\cos \theta +i\sin \theta \right)$ and $Z_2=33\left(\cos \theta +i\sin \theta \right)$ 

Add $Z_1=24\left(\cos \theta +i\sin \theta \right)$ and $Z_2=27\left(\cos \theta +i\sin \theta \right)$ 

Add $Z_1=4\left(\cos \theta -i\sin \theta \right)$ and $Z_2=7\left(\cos \theta -i\sin \theta \right)$ 

Add $Z_1=4\left(\cos \theta +i\sin \theta \right)$ and $Z_2=7\left(\cos \theta +i\sin \theta \right)$ 

Find the sum of $Z_1=3\left(\cos \theta +i\sin \theta \right)$ and $Z_2=2\left(\cos \theta +i\sin \theta \right)$

If $n$ is a positive integer, then ${\left(p+iq\right)}^{\frac{1}{n}}+{\left(p-iq\right)}^{\frac{1}{n}}=$

The polar co-ordinates of a point whose cartesian co-ordinates are $\left(-\frac{1}{\sqrt{2}},-\frac{1}{\sqrt{2}}\right)$ are

If $z=(\cos \theta ,\sin \theta )$, find $\left(z-\frac{1}{z}\right)$