Evaluate
\left(x+\left(-4-4i\right)\right)\left(x+\left(-4+4i\right)\right)
Expand
x^{2}-8x+32
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x^{2}-4x+4ix-4x+16-16i-4ix+16i+16
Apply the distributive property by multiplying each term of x-4-4i by each term of x-4+4i.
x^{2}-4x+4ix-4x-4ix+16+16+\left(-16+16\right)i
Combine the real and imaginary parts.
x^{2}-4x+4ix-4x-4ix+32
Do the additions.
x^{2}+\left(-4+4i\right)x-4x-4ix+32
Combine -4x and 4ix to get \left(-4+4i\right)x.
x^{2}+\left(-8+4i\right)x-4ix+32
Combine \left(-4+4i\right)x and -4x to get \left(-8+4i\right)x.
x^{2}-8x+32
Combine \left(-8+4i\right)x and -4ix to get -8x.
x^{2}-4x+4ix-4x+16-16i-4ix+16i+16
Apply the distributive property by multiplying each term of x-4-4i by each term of x-4+4i.
x^{2}-4x+4ix-4x-4ix+16+16+\left(-16+16\right)i
Combine the real and imaginary parts.
x^{2}-4x+4ix-4x-4ix+32
Do the additions.
x^{2}+\left(-4+4i\right)x-4x-4ix+32
Combine -4x and 4ix to get \left(-4+4i\right)x.
x^{2}+\left(-8+4i\right)x-4ix+32
Combine \left(-4+4i\right)x and -4x to get \left(-8+4i\right)x.
x^{2}-8x+32
Combine \left(-8+4i\right)x and -4ix to get -8x.
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Limits
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