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Q.
Find the multiplicative-inverse of $ 5-6i $
J & K CETJ & K CET 2014
Solution:
Let $ z=5-6i $ then its multiplication inverse, $ {{z}^{-1}}=\frac{{\bar{z}}}{|z{{|}^{2}}} $
$=\frac{5+6i}{{{(5)}^{2}}+{{(-6)}^{2}}}=\frac{5+6i}{25+36} $
$=\frac{5}{61}+\frac{6}{61}i $