WEBVTT
00:00:00.480 --> 00:00:21.320
Simplify four cos of 90 plus π sin of 90 multiplied by five cos of 80 plus π sin 80 multiplied by four cos of 45 plus π sin of 45, giving your answer in trigonometric form.
00:00:21.680 --> 00:00:23.720
Recall the product formula.
00:00:24.200 --> 00:00:45.680
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 can be found by multiplying the moduli and adding the arguments.
00:00:46.160 --> 00:00:53.760
We can extend this to three complex numbers and find the product of the three complex numbers that weβve been given.
00:00:54.000 --> 00:00:55.760
Letβs begin by multiplying their moduli.
00:00:56.120 --> 00:01:01.440
Thatβs four, five, and four, which is 80.
00:01:02.280 --> 00:01:04.520
Next, weβll add their arguments.
00:01:04.880 --> 00:01:12.360
Thatβs 90, 80, and 45, which is 215.
00:01:12.880 --> 00:01:28.760
In trigonometric or polar form then, the product of these three complex numbers is 80 multiplied by cos of 215 degrees plus π sin of 215.