What is (-x^2+sqrt(2)ix+1)^2 ?

The solution to (-x^2+sqrt(2)ix+1)^2 is (x^4-4x^2+1)+(-2sqrt(2)x^3+2sqrt(2)x)i

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simplify (-x^2+sqrt(2)ix+1)^2

simplify

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

(x^{4} - 4 x^{2} + 1) + (- 22 x^{3} + 22 x) i

Solution steps

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

Apply exponent rule:

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

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

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

Distribute parentheses

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

Simplify

- x^{2} (- x^{2}) - x^{2} 2 i x - x^{2} \cdot 1 + 2 i x (- x^{2}) + 2 i x 2 i x + 2 i x \cdot 1 + 1 \cdot (- x^{2}) + 1 \cdot 2 i x + 1 \cdot 1 : x^{4} - 4 x^{2} - 22 x^{3} i + 22 x i + 1

= x^{4} - 4 x^{2} - 22 x^{3} i + 22 x i + 1

Rewrite in standard complex form:

(x^{4} - 4 x^{2} + 1) + (- 22 x^{3} + 22 x) i

= (x^{4} - 4 x^{2} + 1) + (- 22 x^{3} + 22 x) i

tan (x) cos^{2} (x)

\frac{d}{d x} ((y) (x^{2} + 3 x))

(1 - y + 3)^{2}

y cos (t) + 2 t e^{y} (sin (t) + t^{2} e^{y} + 2) \frac{d y}{d t}

cos (\frac{π ( x + 1 )}{8}) + 148 x - 9062

What is (-x^2+sqrt(2)ix+1)^2 ?
The solution to (-x^2+sqrt(2)ix+1)^2 is (x^4-4x^2+1)+(-2sqrt(2)x^3+2sqrt(2)x)i