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

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

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

simplify

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

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

Solution steps

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

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

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

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

Rewrite in standard complex form:

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

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

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

\frac{100 ( 0.02 x + 4 ) ^{3}}{x}

(f \circ g) (2 x - 1) (- x^{2})

\frac{s ^{2} ( s + 1 ) ( s + 30 ) ( s + 40 )}{( s + 2 ) ( s + 3 )}

(a - 12 b) + (- b + 12 a) i

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