Solve (x+ix)*(1-ix)^2

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

Evaluate

$$\left(1+i\right)x\left(1-ix\right)^{2}$$

Solution Steps

Combine x and ix to get \left(1+i\right)x.

$$\left(1+i\right)x\left(1-ix\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1-ix\right)^{2}.

$$\left(1+i\right)x\left(1-2ix-x^{2}\right)$$

Use the distributive property to multiply \left(1+i\right)x by 1-2ix-x^{2}.

$$\left(1+i\right)x+\left(2-2i\right)x^{2}+\left(-1-i\right)x^{3}$$

Expand

$$\left(-1-i\right)x^{3}+\left(2-2i\right)x^{2}+\left(1+i\right)x$$

Solution Steps

Combine x and ix to get \left(1+i\right)x.

$$\left(1+i\right)x\left(1-ix\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(1-ix\right)^{2}.

$$\left(1+i\right)x\left(1-2ix-x^{2}\right)$$

Use the distributive property to multiply \left(1+i\right)x by 1-2ix-x^{2}.

$$\left(1+i\right)x+\left(2-2i\right)x^{2}+\left(-1-i\right)x^{3}$$