What is the geometric interpretation of multiplying two complex numbers?

1 Answer
Wataru
Dec 12, 2014

Let #z_1# and #z_2# be two complex numbers.

By rewriting in exponential form,

#{(z_1=r_1e^{i theta_1}),(z_2=r_2 e^{i theta_2}):}#

So,

#z_1 cdot z_2 =r_1e^{i theta_1}cdot r_2 e^{i theta_2} =(r_1 cdot r_2)e^{i(theta_1+theta_2)}#

Hence, the product of two complex numbers can be geometrically interpreted as the combination of the product of their absolute values (#r_1 cdot r_2#) and the sum of their angles (#theta_1+theta_2#) as shown below.

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I hope that this was clear.

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