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

Simplify

xx + x \cdot 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

(t + \frac{1}{t})^{4}

A (5, - 2) B (- 1, 2)

(2 c + d + e) (2 c + d - e)

\frac{( 2 x + 1 ) ^{3} ( 2 x - 3 ) ^{3}}{( 4 x + 3 ) ^{2} ( x + 1 ) ^{4}}

(- 20 x y^{2} + 6 x) d x + (3 y^{2} - 20 x^{2} y) d y