simplify (x-1-i)^2

Solution

simplify

(x - 1 - i)^{2}

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

Solution steps

(x - 1 - i)^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 1 - i)^{2} = (x - 1 - i) (x - 1 - i)

= (x - 1 - i) (x - 1 - i)

Distribute parentheses

= xx + x (- 1) + x (- i) - 1 \cdot x - 1 \cdot (- 1) - 1 \cdot (- i) - i x - i (- 1) - i (- i)

Simplify

xx + x (- 1) + x (- i) - 1 \cdot x - 1 \cdot (- 1) - 1 \cdot (- i) - i x - i (- 1) - i (- i) : 2 i + x^{2} - 2 x - 2 x i

= 2 i + x^{2} - 2 x - 2 x i

Rewrite in standard complex form:

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

= (x^{2} - 2 x) + (2 - 2 x) i

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

(x + 4)^{2} (\frac{ln ( x + 4 )}{x + 4})^{'} + ln (x + 4)

(2 x + 3 y)^{2}

\frac{- 3 s ^{3} + 7 s ^{2} + 32 s + 16}{s ^{2} ( s ^{2} + 8 )}

cos (\frac{π}{2})