simplify (-2+5i)^2

Solution

simplify

(- 2 + 5 i)^{2}

- 21 - 20 i

Solution steps

(- 2 + 5 i)^{2}

Apply Perfect Square Formula:

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

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

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

Simplify

(- 2)^{2} + 2 (- 2) \cdot 5 i + (5 i)^{2} : - 20 i - 21

= - 20 i - 21

Rewrite in standard complex form:

- 21 - 20 i

= - 21 - 20 i

(1 0^{- 1})^{2}

\frac{3 - 3}{3}

\frac{5}{4} \times 3

+ \frac{20 π}{15}

(144 x^{12})^{\frac{1}{2}}