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

(x - 3) (x + 3)

(cos (x) + sec (x))^{2}

\frac{( k + 1 ) ^{2} ( k + 2 ) ^{2}}{4}

\frac{6}{2} (1 + 2)

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