simplify (4x-5i)^2

Solution

simplify

(4 x - 5 i)^{2}

(16 x^{2} - 25) - 40 x i

Solution steps

(4 x - 5 i)^{2}

Apply Perfect Square Formula:

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

(4 x - 5 i)^{2} = (4 x)^{2} - 2 \cdot 4 x \cdot 5 i + (5 i)^{2}

= (4 x)^{2} - 2 \cdot 4 x \cdot 5 i + (5 i)^{2}

(4 x)^{2} = 16 x^{2}

- 2 \cdot 4 x \cdot 5 i = - 40 x i

(5 i)^{2} = - 25

= 16 x^{2} - 40 x i - 25

Rewrite in standard complex form:

(16 x^{2} - 25) - 40 x i

= (16 x^{2} - 25) - 40 x i

\frac{\partial}{\partial x} ((y) (x^{2} + y^{2}))

\frac{a - bi}{1 + ( a + bi ) ^{2}}

(a^{2} - \frac{1}{a})^{4}

(7) (2 + 23)

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