Solve (x+2+2i)(x-2+2i)

$$( x + 2 + 2 i ) ( x - 2 + 2 i )$$

Evaluate

$$\left(x+\left(-2+2i\right)\right)\left(x+\left(2+2i\right)\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+2+2i by each term of x-2+2i.

$$x^{2}-2x+2ix+2x-4+4i+2ix-4i-4$$

Combine the real and imaginary parts.

$$x^{2}-2x+2ix+2x+2ix-4-4+\left(4-4\right)i$$

Do the additions.

$$x^{2}-2x+2ix+2x+2ix-8$$

Combine -2x and 2ix to get \left(-2+2i\right)x.

$$x^{2}+\left(-2+2i\right)x+2x+2ix-8$$

Combine \left(-2+2i\right)x and 2x to get 2ix.

$$x^{2}+2ix+2ix-8$$

Combine 2ix and 2ix to get 4ix.

$$x^{2}+4ix-8$$

Expand

$$x^{2}+4ix-8$$

Solution Steps

Apply the distributive property by multiplying each term of x+2+2i by each term of x-2+2i.

$$x^{2}-2x+2ix+2x-4+4i+2ix-4i-4$$

Combine the real and imaginary parts.

$$x^{2}-2x+2ix+2x+2ix-4-4+\left(4-4\right)i$$

Do the additions.

$$x^{2}-2x+2ix+2x+2ix-8$$

Combine -2x and 2ix to get \left(-2+2i\right)x.

$$x^{2}+\left(-2+2i\right)x+2x+2ix-8$$

Combine \left(-2+2i\right)x and 2x to get 2ix.

$$x^{2}+2ix+2ix-8$$

Combine 2ix and 2ix to get 4ix.

$$x^{2}+4ix-8$$