Video: Finding the Product of Complex Numbers in Polar Form

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. 𝑍 is equal to π‘Ÿ cos πœƒ plus 𝑖 sin πœƒ, where π‘Ÿ is the modulus and πœƒ 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 π‘Ÿ one and an argument of πœƒ one and 𝑍 two with a modulus of π‘Ÿ two and an argument of πœƒ two, their product, 𝑍 one, 𝑍 two, is given by π‘Ÿ one, π‘Ÿ two multiplied by cos of πœƒ one plus πœƒ two plus 𝑖 sin of πœƒ one plus πœƒ two.

To find the modulus of their product, we multiply together the moduli of the two complex numbers, π‘Ÿ one multiplied by π‘Ÿ 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.

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