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 \cdot 4 + x (- 3 i) + 4 x + 4 \cdot 4 + 4 (- 3 i) - 3 i x - 3 i 4 - 3 i (- 3 i)

Simplify

xx + x \cdot 4 + x (- 3 i) + 4 x + 4 \cdot 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

\frac{5 ( 5 + 897 )}{109}

- \frac{10 sin ( x )}{( 2 - 3 cos ( x ) ) ^{2}}

A (2, - 11) y B (- 1, - 5)

(x + (\frac{2}{3})) (x + 7)

(2 y - y^{'} (t))^{3}