Imaginary and complex numbers

Use your imagination and complexity (?) and dive into the world of complex numbers. Add, subtract, multiply, & divide complex numbers. Plot them on the complex plane and convert between rectangular and polar forms.
19 exercises available

Learn how we can visualize complex numbers in a plane. This can be seen as an expansion of the 1-dimensional real number line into a 2-dimensional plane!

Learn how to multiply complex numbers using the fact that i^2=-1 and the distributive property. For example, multiply (1+i) by (2+3i).

Learn how to divide complex numbers using the conjugate of the divisor. For example, divide (2+3i) by (-1+4i) by multiplying both the dividend and the divisor by (-1-4i).

Learn how to represent complex numbers in a different way. Unlike rectangular form, which emphasizes the real and imaginary parts, polar form emphasizes the absolute value ("modulus") and the angle ("argument").

This tutorial goes through a fancy problem from the IIT JEE exam in India (competitive exam for getting into their top engineering schools). Whether or not you live in India, this is a good example to test whether you are a complex number rock star.