What is 1/((8+6i)^2) ?

The solution to 1/((8+6i)^2) is 7/2500-6/625 i

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simplify 1/((8+6i)^2)

simplify

\frac{1}{( 8 + 6 i ) ^{2}}

\frac{7}{2500} - \frac{6}{625} i

Solution steps

\frac{1}{( 8 + 6 i ) ^{2}}

Expand

(8 + 6 i)^{2} : 96 i + 28

= \frac{1}{96 i + 28}

Rewrite

96 i + 28

in standard complex form:

28 + 96 i

= \frac{1}{28 + 96 i}

Multiply by the conjugate

\frac{28 - 96 i}{28 - 96 i}

= \frac{1 \cdot ( 28 - 96 i )}{( 28 + 96 i ) ( 28 - 96 i )}

Simplify

\frac{1 \cdot ( 28 - 96 i )}{( 28 + 96 i ) ( 28 - 96 i )} : \frac{28 - 96 i}{10000}

= \frac{28 - 96 i}{10000}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

= \frac{28}{10000} + \frac{- 96}{10000} i

Simplify

\frac{28}{10000} + \frac{- 96}{10000} i : \frac{7}{2500} - \frac{6}{625} i

= \frac{7}{2500} - \frac{6}{625} i

2 \times \frac{3}{2}

\frac{1}{sin ^{2} ( x )} - 1

\frac{1}{( - 3.999 ) ^{2} - 16}

- 2 (7)

3 x \cdot 6