Evaluate
\left(x+\left(5-3i\right)\right)\left(x+\left(5+3i\right)\right)
Expand
x^{2}+10x+34
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x^{2}+5x-3ix+5x+25-15i+3ix+15i+9
Apply the distributive property by multiplying each term of x+5+3i by each term of x+5-3i.
x^{2}+5x-3ix+5x+3ix+25+9+\left(-15+15\right)i
Combine the real and imaginary parts.
x^{2}+5x-3ix+5x+3ix+34
Do the additions.
x^{2}+\left(5-3i\right)x+5x+3ix+34
Combine 5x and -3ix to get \left(5-3i\right)x.
x^{2}+\left(10-3i\right)x+3ix+34
Combine \left(5-3i\right)x and 5x to get \left(10-3i\right)x.
x^{2}+10x+34
Combine \left(10-3i\right)x and 3ix to get 10x.
x^{2}+5x-3ix+5x+25-15i+3ix+15i+9
Apply the distributive property by multiplying each term of x+5+3i by each term of x+5-3i.
x^{2}+5x-3ix+5x+3ix+25+9+\left(-15+15\right)i
Combine the real and imaginary parts.
x^{2}+5x-3ix+5x+3ix+34
Do the additions.
x^{2}+\left(5-3i\right)x+5x+3ix+34
Combine 5x and -3ix to get \left(5-3i\right)x.
x^{2}+\left(10-3i\right)x+3ix+34
Combine \left(5-3i\right)x and 5x to get \left(10-3i\right)x.
x^{2}+10x+34
Combine \left(10-3i\right)x and 3ix to get 10x.
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