What is a/((2-bi)^2) ?

The solution to a/((2-bi)^2) is (a((4-b^2)+4bi))/(b^4+8b^2+16)

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simplify a/((2-bi)^2)

simplify

\frac{a}{( 2 - bi ) ^{2}}

\frac{a ( ( 4 - b ^{2} ) + 4 bi )}{b ^{4} + 8 b ^{2} + 16}

Solution steps

\frac{a}{( 2 - bi ) ^{2}}

Expand

(2 - bi)^{2} : 4 - 4 bi - b^{2}

= \frac{a}{4 - 4 bi - b ^{2}}

Rewrite

4 - 4 bi - b^{2}

in standard complex form:

(4 - b^{2}) - 4 bi

= \frac{a}{( 4 - b ^{2} ) - 4 bi}

Multiply by the conjugate

\frac{( 4 - b ^{2} ) + 4 bi}{( 4 - b ^{2} ) + 4 bi}

= \frac{a ( ( 4 - b ^{2} ) + 4 bi )}{( ( 4 - b ^{2} ) - 4 bi ) ( ( 4 - b ^{2} ) + 4 bi )}

Simplify

\frac{a ( ( 4 - b ^{2} ) + 4 bi )}{( ( 4 - b ^{2} ) - 4 bi ) ( ( 4 - b ^{2} ) + 4 bi )} : \frac{a ( ( 4 - b ^{2} ) + 4 bi )}{b ^{4} + 8 b ^{2} + 16}

= \frac{a ( ( 4 - b ^{2} ) + 4 bi )}{b ^{4} + 8 b ^{2} + 16}

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What is a/((2-bi)^2) ?
The solution to a/((2-bi)^2) is (a((4-b^2)+4bi))/(b^4+8b^2+16)