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 realclass 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, z_{1} = r_{1} (cos
_{1} + i sin
_{1}) and z_{2} = r_{2} (cos
_{2} + i sin
_{2}),
the product of these numbers is z_{1 }x z_{2} = r_{1}r_{2}[cos
(_{1} +
_{2}) + i sin
(_{1} +
_{2} )]. (More text below video...)
(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 z_{1} = cos 120
+ i sin 120
and z_{2} = cos 100
+ i sin 100, the first
thing you need to note is that r_{1}, r_{2} both
are 1,
_{1} is 120
and
_{2} is 100. Plug in the values
in z_{1}z_{2 }= r_{1}r_{2}[cos
(_{1} +
_{2}) + i sin
(_{1} +
_{2})], and
it yields the product z_{1}z_{2} = cos (220) + i sin (220).
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