Evaluate
\left(x+\left(3-8i\right)\right)\left(x+\left(3+8i\right)\right)
Expand
x^{2}+6x+73
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x^{2}+3x-8ix+3x+9-24i+8ix+24i+64
Apply the distributive property by multiplying each term of x+3+8i by each term of x+3-8i.
x^{2}+3x-8ix+3x+8ix+9+64+\left(-24+24\right)i
Combine the real and imaginary parts.
x^{2}+3x-8ix+3x+8ix+73
Do the additions.
x^{2}+\left(3-8i\right)x+3x+8ix+73
Combine 3x and -8ix to get \left(3-8i\right)x.
x^{2}+\left(6-8i\right)x+8ix+73
Combine \left(3-8i\right)x and 3x to get \left(6-8i\right)x.
x^{2}+6x+73
Combine \left(6-8i\right)x and 8ix to get 6x.
x^{2}+3x-8ix+3x+9-24i+8ix+24i+64
Apply the distributive property by multiplying each term of x+3+8i by each term of x+3-8i.
x^{2}+3x-8ix+3x+8ix+9+64+\left(-24+24\right)i
Combine the real and imaginary parts.
x^{2}+3x-8ix+3x+8ix+73
Do the additions.
x^{2}+\left(3-8i\right)x+3x+8ix+73
Combine 3x and -8ix to get \left(3-8i\right)x.
x^{2}+\left(6-8i\right)x+8ix+73
Combine \left(3-8i\right)x and 3x to get \left(6-8i\right)x.
x^{2}+6x+73
Combine \left(6-8i\right)x and 8ix to get 6x.
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