simplify (x+ix^2)^2

Solution

simplify

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

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

Solution steps

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

Apply Perfect Square Formula:

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

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

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

2 x i x^{2} = 2 x^{3} i

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

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

Rewrite in standard complex form:

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

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

\frac{3 ( 2 x - 3 y )}{( 2 x + 3 y )}

\frac{2 x ^{2} + 6 x}{( x + 2 ) ( x + 4 )}

1 - 2 (x + h) - 1 - 2 x

I n (e^{x} - e)

200 x - 10 (x - 10) (\frac{x - 10}{2}) - 100 (x - 20)