Solve (x-3+3i)(x-3-3i)

$$( x - 3 + 3 i ) ( x - 3 - 3 i )$$

Evaluate

$$\left(x+\left(-3-3i\right)\right)\left(x+\left(-3+3i\right)\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-3+3i by each term of x-3-3i.

$$x^{2}-3x-3ix-3x+9+9i+3ix-9i+9$$

Combine the real and imaginary parts.

$$x^{2}-3x-3ix-3x+3ix+9+9+\left(9-9\right)i$$

Do the additions.

$$x^{2}-3x-3ix-3x+3ix+18$$

Combine -3x and -3ix to get \left(-3-3i\right)x.

$$x^{2}+\left(-3-3i\right)x-3x+3ix+18$$

Combine \left(-3-3i\right)x and -3x to get \left(-6-3i\right)x.

$$x^{2}+\left(-6-3i\right)x+3ix+18$$

Combine \left(-6-3i\right)x and 3ix to get -6x.

$$x^{2}-6x+18$$

Expand

$$x^{2}-6x+18$$

Solution Steps

Apply the distributive property by multiplying each term of x-3+3i by each term of x-3-3i.

$$x^{2}-3x-3ix-3x+9+9i+3ix-9i+9$$

Combine the real and imaginary parts.

$$x^{2}-3x-3ix-3x+3ix+9+9+\left(9-9\right)i$$

Do the additions.

$$x^{2}-3x-3ix-3x+3ix+18$$

Combine -3x and -3ix to get \left(-3-3i\right)x.

$$x^{2}+\left(-3-3i\right)x-3x+3ix+18$$

Combine \left(-3-3i\right)x and -3x to get \left(-6-3i\right)x.

$$x^{2}+\left(-6-3i\right)x+3ix+18$$

Combine \left(-6-3i\right)x and 3ix to get -6x.

$$x^{2}-6x+18$$