Question

Find the multiplicative inverse of (6+5i) 2

Answer 1

$\textbf{Given:}$

$(6+5i)^2$

$\textbf{To find: Multiplicative inverse of (6+5i)^2 }$

$(6+5i)^2$

$=6^2+(5i)^2+60\;i$

$=36-25+60\;i$

$=11+60\;i$

$\text{Now,}$

$\text{Multiplicative inverse of (6+5i)^2 }$

$=\displaystyle\frac{1}{(6+5i)^2}$

$=\displaystyle\frac{1}{11+60i}$

$\text{Multiply both numerator and}\;$$\;\;\;\text{denominator by 11-60i}$

$=\displaystyle\frac{1}{11+60i}{\times}\frac{11-60i}{11-60i}$

$=\displaystyle\frac{11-60i}{(11)^2-(60i)^2}$

$=\displaystyle\frac{11-60i}{121+3600}$

$=\displaystyle\frac{11-60i}{3721}$

$\therefore\textbf{The multiplicative inverse of \bf(6+5i)^2 is \bf\displaystyle\frac{11-60i}{3721} }$

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Answer 2

Answer:

Step-by-step explanation: