Evaluate
\left(X+\left(-1-i\right)\right)\left(X+\left(-1+i\right)\right)
Expand
X^{2}-2X+2
Share
Copied to clipboard
X^{2}-X+iX-X+1-i-iX+i+1
Apply the distributive property by multiplying each term of X-1-i by each term of X-1+i.
X^{2}-X+iX-X-iX+1+1+\left(-1+1\right)i
Combine the real and imaginary parts.
X^{2}-X+iX-X-iX+2
Do the additions.
X^{2}+\left(-1+i\right)X-X-iX+2
Combine -X and iX to get \left(-1+i\right)X.
X^{2}+\left(-2+i\right)X-iX+2
Combine \left(-1+i\right)X and -X to get \left(-2+i\right)X.
X^{2}-2X+2
Combine \left(-2+i\right)X and -iX to get -2X.
X^{2}-X+iX-X+1-i-iX+i+1
Apply the distributive property by multiplying each term of X-1-i by each term of X-1+i.
X^{2}-X+iX-X-iX+1+1+\left(-1+1\right)i
Combine the real and imaginary parts.
X^{2}-X+iX-X-iX+2
Do the additions.
X^{2}+\left(-1+i\right)X-X-iX+2
Combine -X and iX to get \left(-1+i\right)X.
X^{2}+\left(-2+i\right)X-iX+2
Combine \left(-1+i\right)X and -X to get \left(-2+i\right)X.
X^{2}-2X+2
Combine \left(-2+i\right)X and -iX to get -2X.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}