simplify (2x-5i)^2

Solution

simplify

(2 x - 5 i)^{2}

(4 x^{2} - 25) - 20 x i

Solution steps

(2 x - 5 i)^{2}

Apply Perfect Square Formula:

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

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

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

(2 x)^{2} = 4 x^{2}

- 2 \cdot 2 x \cdot 5 i = - 20 x i

(5 i)^{2} = - 25

= 4 x^{2} - 20 x i - 25

Rewrite in standard complex form:

(4 x^{2} - 25) - 20 x i

= (4 x^{2} - 25) - 20 x i

- \frac{- s ^{2} + 1}{( s ^{2} + 1 ) ^{2}}

(- 4 x^{3} + 3 y) \frac{d x}{d y}

x y d x - (x^{2} + 3 y^{2}) d y

(x + i y)^{6} + (x + i y)^{3} - 1

\frac{n ^{2 n}}{( n + 1 ) ^{2 (n + 1)}}