Question

Find the multiplicative-inverse of $5-6i$

• A. $-(5/61)+(6/61)i$
• B. $(5/61)+(6/61)i$
• C. $(5/61)-(6/61)i$
• D. $-(5/61)-(6/61)i$

Answer 1

Answer: (B)

Let $z=5-6i$ then its multiplication inverse, $z^{-1}=\frac{\bar{z}}{|z{|}^2}$
$=\frac{5+6i}{{(5)}^2+{(-6)}^2}=\frac{5+6i}{25+36}$
$=\frac{5}{61}+\frac{6}{61}i$