simplify (2x-3i)^2

Solution

simplify

(2 x - 3 i)^{2}

(4 x^{2} - 9) - 12 x i

Solution steps

(2 x - 3 i)^{2}

Apply Perfect Square Formula:

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

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

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

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

- 2 \cdot 2 x \cdot 3 i = - 12 x i

(3 i)^{2} = - 9

= 4 x^{2} - 12 x i - 9

Rewrite in standard complex form:

(4 x^{2} - 9) - 12 x i

= (4 x^{2} - 9) - 12 x i

(5 x + 4 + 14)^{2}

\frac{- 1}{3} 3^{2} + \frac{2}{3} 3 + \frac{8}{3}

(e^{- x} + 1)^{2}

x^{\frac{1}{3}} \cdot (x - 2)^{2}

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