What is ((2-3i)^2)/((8+6i)^2) ?

The solution to ((2-3i)^2)/((8+6i)^2) is -323/2500+i 9/625

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simplify ((2-3i)^2)/((8+6i)^2)

simplify

\frac{( 2 - 3 i ) ^{2}}{( 8 + 6 i ) ^{2}}

- \frac{323}{2500} + i \frac{9}{625}

Solution steps

\frac{( 2 - 3 i ) ^{2}}{( 8 + 6 i ) ^{2}}

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

= \frac{( 2 - 3 i ) ^{2}}{28 + 96 i}

(2 - 3 i)^{2} = - 5 - 12 i

= \frac{( - 5 - 12 i )}{28 + 96 i}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = - 5, b = - 12, c = 28, d = 96

= \frac{( - 5 \cdot 28 + ( - 12 ) \cdot 96 ) + ( - 12 \cdot 28 - ( - 5 ) \cdot 96 ) i}{2 8 ^{2} + 9 6 ^{2}}

Refine

= \frac{- 1292 + 144 i}{10000}

Simplify

\frac{- 1292 + 144 i}{10000} : \frac{- 323 + 36 i}{2500}

= \frac{- 323 + 36 i}{2500}

Rewrite

\frac{- 323 + 36 i}{2500}

in standard complex form:

- \frac{323}{2500} + \frac{9}{625} i

= - \frac{323}{2500} + \frac{9}{625} i

(\frac{1}{4})^{2} - 4

6 x (x - 1) = 12 - 7 x

\frac{( 3 x ^{5} y ^{3} ) ^{5}}{( 6 x ^{10} y ^{7} ) ^{2}}

i^{51}

216 + 27 y^{12}

What is ((2-3i)^2)/((8+6i)^2) ?
The solution to ((2-3i)^2)/((8+6i)^2) is -323/2500+i 9/625