simplify (x-2+i)^2

Solution

simplify

(x - 2 + i)^{2}

(x^{2} - 4 x + 3) + (- 4 + 2 x) i

Solution steps

(x - 2 + i)^{2}

Apply exponent rule:

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

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

= (x - 2 + i) (x - 2 + i)

Distribute parentheses

= xx + x (- 2) + x i - 2 x - 2 (- 2) - 2 i + i x + i (- 2) + ii

Simplify

xx + x (- 2) + x i - 2 x - 2 (- 2) - 2 i + i x + i (- 2) + ii : - 4 i + x^{2} - 4 x + 2 x i + 3

= - 4 i + x^{2} - 4 x + 2 x i + 3

Rewrite in standard complex form:

(x^{2} - 4 x + 3) + (- 4 + 2 x) i

= (x^{2} - 4 x + 3) + (- 4 + 2 x) i

(1250 - x) + (- \frac{5100}{( 0.02 x + 1 ) ^{2}})

\frac{- x ^{2} + 12 x - 35}{( x ^{2} - 6 x + 1 ) ^{2}}

(2 x - 4) (2 x^{2} - 8 x + 35)^{4} d x

\frac{1250 x + 750}{( 25 x ^{2} - 30 x + 9 ) ^{2}}

\frac{x ^{2} - 10 x - 41}{( x + 1 ) ( x + 4 ) ( x - 1 )}