simplify (1+ix)^2

Solution

simplify

(1 + i x)^{2}

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

Solution steps

(1 + i x)^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(1 + i x)^{2} = 1^{2} + 2 \cdot 1 i x + (i x)^{2}

= 1^{2} + 2 \cdot 1 i x + (i x)^{2}

1^{2} = 1

2 \cdot 1 i x = 2 x i

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

= 1 + 2 x i - x^{2}

Rewrite in standard complex form:

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

= (1 - x^{2}) + 2 x i

(2 e^{x^{2}} + x^{2})^{3}

(1 + x + x^{2})^{8}

3 (3 - 2)

\frac{s + 1}{s ^{2} ( s + 2 ) ^{3}}

\frac{d ^{2}}{d k ^{2}} ((y (k, x)) (e^{4 x} - k x))