simplify (a+bi+1)^2

Solution

simplify

(a + bi + 1)^{2}

(a^{2} + 2 a - b^{2} + 1) + (2 b + 2 ab) i

Solution steps

(a + bi + 1)^{2}

Apply exponent rule:

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

(a + bi + 1)^{2} = (a + bi + 1) (a + bi + 1)

= (a + bi + 1) (a + bi + 1)

Distribute parentheses

= aa + abi + a \cdot 1 + bia + bibi + bi 1 + 1 \cdot a + 1 \cdot bi + 1 \cdot 1

Simplify

aa + abi + a \cdot 1 + bia + bibi + bi 1 + 1 \cdot a + 1 \cdot bi + 1 \cdot 1 : a^{2} + 2 bi + 2 abi + 2 a - b^{2} + 1

= a^{2} + 2 bi + 2 abi + 2 a - b^{2} + 1

Rewrite in standard complex form:

(a^{2} + 2 a - b^{2} + 1) + (2 b + 2 ab) i

= (a^{2} + 2 a - b^{2} + 1) + (2 b + 2 ab) i

(x^{2} + 3 - 2) \times (x^{2} + 3 + 2)

\frac{( t - 3 ) ^{2}}{4}

A (- 1, 8) e B (- 5, - 1)

1400 (7 - x) + 2800 9 + x^{2}

6 (x + 3 = 5 x + 1)