simplify (a-ib)^2

Solution

simplify

(a - ib)^{2}

(a^{2} - b^{2}) - 2 abi

Solution steps

(a - ib)^{2}

Apply Perfect Square Formula:

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

(a - ib)^{2} = a^{2} - 2 aib + (ib)^{2}

= a^{2} - 2 aib + (ib)^{2}

- 2 aib = - 2 abi

(ib)^{2} = - b^{2}

= a^{2} - 2 abi - b^{2}

Rewrite in standard complex form:

(a^{2} - b^{2}) - 2 abi

= (a^{2} - b^{2}) - 2 abi

(6 - 5 y i)^{2}

\frac{d ^{2}}{d x ^{2}} ((y) (- x^{2} y^{3} + 4 x y^{2} + 12 x y))

(3 + x 2)^{2}

5^{2}