WEBVTT
00:00:00.760 --> 00:00:04.760
What do we need to do to multiply two complex numbers in polar form?
00:00:05.680 --> 00:00:08.960
A complex number in polar form looks like this.
00:00:09.480 --> 00:00:16.520
π is equal to π cos π plus π sin π, where π is the modulus and π is the argument.
00:00:17.080 --> 00:00:19.080
Next, letβs recall the product formula.
00:00:19.600 --> 00:00:47.440
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.
00:00:48.280 --> 00:00:54.560
To find the modulus of their product, we multiply together the moduli of the two complex numbers, π one multiplied by π two.
00:00:54.960 --> 00:00:59.960
And to find the argument of the product, we added together the arguments of π one and π two.
00:01:00.680 --> 00:01:09.520
We can see then that, to multiply two complex numbers in polar form, we multiply their moduli together and we add their arguments.