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What is the product theorem of complex numbers in polar form?

1 Answer

Mar 7, 2018

$z w = (r_{1} \cdot r_{2}) (cos (θ_{1} + θ_{2}) + i sin (θ_{1} + θ_{2}))$ $zw = (r_1 *r_2)(cos(theta_1 +theta_2) + isin(theta_1 +theta_2))$

Explanation:

Alright, so the polar form of a complex number $z = a + b i$ $z=a+bi$ is

$z = r (cos (θ) + i sin (θ))$ $z= r(cos(theta) + isin(theta))$

Suppose you have a complex number $w$ $w$ which you wanted to multiply by $z$ $z$ , then this will be the rule you need to use

$z w = (r_{1} \cdot r_{2}) (cos (θ_{1} + θ_{2}) + i sin (θ_{1} + θ_{2}))$ $zw = (r_1 *r_2)(cos(theta_1 +theta_2) + isin(theta_1 +theta_2))$

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