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

The solution to (5/3-2/3 i)^2 is 7/3-20/9 i

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simplify (5/3-2/3 i)^2

simplify

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

\frac{7}{3} - \frac{20}{9} i

Solution steps

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

Apply Perfect Square Formula:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

(\frac{5}{3} - \frac{2}{3} i)^{2} = (\frac{5}{3})^{2} - 2 \cdot \frac{5}{3} \cdot \frac{2}{3} i + (\frac{2}{3} i)^{2}

= (\frac{5}{3})^{2} - 2 \cdot \frac{5}{3} \cdot \frac{2}{3} i + (\frac{2}{3} i)^{2}

Simplify

(\frac{5}{3})^{2} - 2 \cdot \frac{5}{3} \cdot \frac{2}{3} i + (\frac{2}{3} i)^{2} : \frac{7}{3} - \frac{20}{9} i

= \frac{7}{3} - \frac{20}{9} i

a + (a - b) + (- a + b)

2 (5 x + 4) + 3 (2 x - 1)

\frac{- 2 x - 2}{x ^{2} + 2 x - 8} - \frac{x - 1}{2 - x}

2 x^{2} \times x

x + 5 x