What is ((5-14i)/(2-10i))^2+(2+3i)^2 ?

The solution to ((5-14i)/(2-10i))^2+(2+3i)^2 is -501/169+17049/1352 i

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simplify ((5-14i)/(2-10i))^2+(2+3i)^2

simplify

(\frac{5 - 14 i}{2 - 10 i})^{2} + (2 + 3 i)^{2}

- \frac{501}{169} + \frac{17049}{1352} i

Solution steps

(\frac{5 - 14 i}{2 - 10 i})^{2} + (2 + 3 i)^{2}

(\frac{5 - 14 i}{2 - 10 i})^{2} = \frac{825 i + 2752}{1352}

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

= \frac{825 i + 2752}{1352} + 12 i - 5

Join

\frac{825 i + 2752}{1352} + 12 i - 5 : \frac{17049 i - 4008}{1352}

= \frac{17049 i - 4008}{1352}

Rewrite

17049 i - 4008

in standard complex form:

- 4008 + 17049 i

= \frac{- 4008 + 17049 i}{1352}

Apply the fraction rule:

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

= \frac{- 4008}{1352} + \frac{17049}{1352} i

Cancel

\frac{- 4008}{1352} : - \frac{501}{169}

= - \frac{501}{169} + \frac{17049}{1352} i

\frac{3 7 - 5}{7 - 2}

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\frac{( 6 x ^{3} + 11 x ^{2} - 47 x + 20 )}{( 2 x ^{2} + 7 x - 4 )}

2 x^{2} + 6 x + 2

- 2 \cdot 2 x

What is ((5-14i)/(2-10i))^2+(2+3i)^2 ?
The solution to ((5-14i)/(2-10i))^2+(2+3i)^2 is -501/169+17049/1352 i