Trigonometry: Multiplication of Complex Numbers
This is a free lesson from our course in Trigonometry
 
   
In this lesson you'll learn how to multiply complex numbers written in trigonometric form. It shall be explained by the instructor with the help of some examples, practice questions with solution and using video that brings in an element of real-class room experience. Here you are presented the theorem relating to multiplying two complex numbers in polar form. It states that if we have two complex numbers,
     z1 = r1 (cos 1 + i sin 1) and
     z2 = r2 (cos 2 + i sin 2),
the product of these numbers is
     z1 x z2 = r1r2[cos (1 + 2) + i sin (1 + 2 )].
(More text below video...)
<h2> Trigonometry - Multiplication of Complex Numbers</h2> <p> Multiplication, complex numbers, number, trigonometry help, multiplying, polar form, multiplying complex numbers, value, theorem, examples, solution, imaginary number, rectangular form, homework help, practice questions, quizzes.</p> <p> It states that if we have two complex numbers, z1 = r1 (cos (theta)1 + i sin (theta)1) and z2 = r2 (cos (theta)2 + i sin (theta)2), the product of these numbers is z1 x z2 = r1r2[cos ((theta)1 + (theta)2) + i sin ((theta)1 + (theta)2)]. </p>
Other useful lessons:
The Complex Number System
Polar Form of Complex Numbers

(Continued from above) Rule for multiplying two complex numbers in polar form:
multiply the moduli.
add the arguments.

For example, to multiply the complex numbers z1 = cos 120 + i sin 120 and z2 = cos 100 + i sin 100, the first thing you need to note is that r1, r2 both are 1, 1 is 120 and 2 is 100. Plug in the values in z1z= r1r2[cos (1 + 2) + i sin (1 + 2)], and it yields the product  z1z2 = cos (220) + i sin (220).

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