Question Video: Finding the Product of Complex Numbers in Polar Form | Nagwa Question Video: Finding the Product of Complex Numbers in Polar Form | Nagwa

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

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

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### 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. π is equal to π cos π plus π sin π, where π is the modulus and π is the argument. Next, letβs recall the product formula. This says that, for two complex numbers expressed in polar form, π one with a modulus of π one and an argument of π one and π two with a modulus of π two and an argument of π two, their product, π one, π two, is given by π one, π two multiplied by cos of π one plus π two plus π sin of π one plus π two.

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

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