simplify (-5+10i)^2

Solution

simplify

(- 5 + 10 i)^{2}

- 75 - 100 i

Solution steps

(- 5 + 10 i)^{2}

Apply Perfect Square Formula:

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

(- 5 + 10 i)^{2} = (- 5)^{2} + 2 (- 5) \cdot 10 i + (10 i)^{2}

= (- 5)^{2} + 2 (- 5) \cdot 10 i + (10 i)^{2}

Simplify

(- 5)^{2} + 2 (- 5) \cdot 10 i + (10 i)^{2} : - 100 i - 75

= - 100 i - 75

Rewrite in standard complex form:

- 75 - 100 i

= - 75 - 100 i

(8 x^{2} - 2 x + 1) - (3 x^{2} + 5 x - 8)

(- 2 - 6 i) - (- 2 - 4 i)

lo g_{\frac{2}{5}} (\frac{125}{8})

\frac{2}{3}

\frac{m ^{2} - n ^{2}}{( m + n ) ^{2}}