Evaluate
\left(x+\left(-5-2i\right)\right)\left(x+\left(-5+2i\right)\right)
Expand
x^{2}-10x+29
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x^{2}-5x-2ix-5x+25+10i+2ix-10i+4
Apply the distributive property by multiplying each term of x-5+2i by each term of x-5-2i.
x^{2}-5x-2ix-5x+2ix+25+4+\left(10-10\right)i
Combine the real and imaginary parts.
x^{2}-5x-2ix-5x+2ix+29
Do the additions.
x^{2}+\left(-5-2i\right)x-5x+2ix+29
Combine -5x and -2ix to get \left(-5-2i\right)x.
x^{2}+\left(-10-2i\right)x+2ix+29
Combine \left(-5-2i\right)x and -5x to get \left(-10-2i\right)x.
x^{2}-10x+29
Combine \left(-10-2i\right)x and 2ix to get -10x.
x^{2}-5x-2ix-5x+25+10i+2ix-10i+4
Apply the distributive property by multiplying each term of x-5+2i by each term of x-5-2i.
x^{2}-5x-2ix-5x+2ix+25+4+\left(10-10\right)i
Combine the real and imaginary parts.
x^{2}-5x-2ix-5x+2ix+29
Do the additions.
x^{2}+\left(-5-2i\right)x-5x+2ix+29
Combine -5x and -2ix to get \left(-5-2i\right)x.
x^{2}+\left(-10-2i\right)x+2ix+29
Combine \left(-5-2i\right)x and -5x to get \left(-10-2i\right)x.
x^{2}-10x+29
Combine \left(-10-2i\right)x and 2ix to get -10x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}