How to multiply and divide by complex numbers

Multiplying and dividing by complex numbers is very similar to how you have learned how to multiply and divide surds (numbers with a rational and irrational part) in GCSE and early A-Level. Take two complex numbers, written a+bi and c+di. To multiply together, treat i as you would treat x with multiplication of an algebraic expression. The only difference is remembering that with complex numbers, i^2 = -1. So replace your i^2 term with -1 and simplify.For division, remember how you treat the denominator with surds. For (a+bi)/(c+di), we take what is known as the conjugate of the denominator, c-di. This, when multiplying through the numerator and denominator, will cancel out the complex part in the denominator, leaving our number will a complex numerator and real denominator. This is a much more useful form to have for a complex number, as it makes it easier to perform operations and to visually examine the number.