simplify (x-3i-2)^2

Solution

simplify

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

(x^{2} - 4 x - 5) + (12 - 6 x) i

Solution steps

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

Apply exponent rule:

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

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

= (x - 3 i - 2) (x - 3 i - 2)

Distribute parentheses

= xx + x (- 3 i) + x (- 2) - 3 i x - 3 i (- 3 i) - 3 i (- 2) - 2 x - 2 (- 3 i) - 2 (- 2)

Simplify

xx + x (- 3 i) + x (- 2) - 3 i x - 3 i (- 3 i) - 3 i (- 2) - 2 x - 2 (- 3 i) - 2 (- 2) : 12 i + x^{2} - 6 x i - 4 x - 5

= 12 i + x^{2} - 6 x i - 4 x - 5

Rewrite in standard complex form:

(x^{2} - 4 x - 5) + (12 - 6 x) i

= (x^{2} - 4 x - 5) + (12 - 6 x) i

\frac{1800 x ^{2} - 300 x + 13}{( - 10 x + 1 ) ^{2} ( - 15 x + 1 ) ^{2}}

\frac{x ( x - 4 ) ( x - 9 )}{24}

2 (\frac{2 π ^{4}}{5} - \frac{x ^{4}}{36})

9 \cdot (x + \frac{1}{3})

\frac{( x ^{2} - 1 ) ln ( z )}{2}