Question Video: Finding the Product of Complex Numbers in Polar Form Mathematics • Third Year of Secondary School

Video Transcript

What do we need to do to multiply two complex numbers in polar form?

A complex number in polar form looks like this. 𝑍 is equal to 𝑟 cos 𝜃 plus 𝑖 sin 𝜃, where 𝑟 is the modulus and 𝜃 is the argument. Next, let’s recall the product formula. This says that, for two complex numbers expressed in polar form, 𝑍 one with a modulus of 𝑟 one and an argument of 𝜃 one and 𝑍 two with a modulus of 𝑟 two and an argument of 𝜃 two, their product, 𝑍 one, 𝑍 two, is given by 𝑟 one, 𝑟 two multiplied by cos of 𝜃 one plus 𝜃 two plus 𝑖 sin of 𝜃 one plus 𝜃 two.

To find the modulus of their product, we multiply together the moduli of the two complex numbers, 𝑟 one multiplied by 𝑟 two. And to find the argument of the product, we added together the arguments of 𝑍 one and 𝑍 two. We can see then that, to multiply two complex numbers in polar form, we multiply their moduli together and we add their arguments.