simplify (x-4-3i)^2

Solution

simplify

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

(x^{2} - 8 x + 7) + (24 - 6 x) i

Solution steps

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

Apply exponent rule:

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

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

= (x - 4 - 3 i) (x - 4 - 3 i)

Distribute parentheses

= xx + x (- 4) + x (- 3 i) - 4 x - 4 (- 4) - 4 (- 3 i) - 3 i x - 3 i (- 4) - 3 i (- 3 i)

Simplify

xx + x (- 4) + x (- 3 i) - 4 x - 4 (- 4) - 4 (- 3 i) - 3 i x - 3 i (- 4) - 3 i (- 3 i) : 24 i + x^{2} - 8 x - 6 x i + 7

= 24 i + x^{2} - 8 x - 6 x i + 7

Rewrite in standard complex form:

(x^{2} - 8 x + 7) + (24 - 6 x) i

= (x^{2} - 8 x + 7) + (24 - 6 x) i

(23)^{2} + 2^{2}

(50 - \frac{q}{2} = \frac{9}{4} 300 - 4 p) (75 - \frac{q}{4})

, 5 (5 - x) + 3 (5 - x)^{2} + 3 x + 2 x^{3}

d x (\frac{1}{15} arcsec (\frac{x}{5}) + c)