How do I find the quotient of two complex numbers in polar form?

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Answer 1 · 2014-10-18T13:31:41

If complex numbers #z_1# and #z_2# in polar form are

#{(z_1=r_1(costheta_1+isin theta_1)),(z_2=r_2(cos theta_2+i sin theta_2)):}#,

then we can write in exponential form

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

So, the quotient #z_1/z_2# can be written as

#z_1/z_2={r_1e^{i theta_1}}/{r_2e^{i theta_2}}=r_1/r_2e^{i(theta_1-theta_2)}#

#=r_1/r_2[cos(theta_1-theta_2)+isin(theta_1-theta_2)]#

I hope that this was helpful.