Evaluate
-2
Real Part
-2
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\frac{-\left(i^{99}-i^{98}\right)}{i^{99}-i^{98}}+\frac{i^{100}-i^{99}}{i^{98}-i^{97}}
Extract the negative sign in i^{101}-i^{100}.
-1+\frac{i^{100}-i^{99}}{i^{98}-i^{97}}
Cancel out i^{99}-i^{98} in both numerator and denominator.
-1+\frac{-\left(i^{98}-i^{97}\right)}{i^{98}-i^{97}}
Extract the negative sign in i^{100}-i^{99}.
-1-1
Cancel out i^{98}-i^{97} in both numerator and denominator.
-2
Subtract 1 from -1 to get -2.
Re(\frac{-\left(i^{99}-i^{98}\right)}{i^{99}-i^{98}}+\frac{i^{100}-i^{99}}{i^{98}-i^{97}})
Extract the negative sign in i^{101}-i^{100}.
Re(-1+\frac{i^{100}-i^{99}}{i^{98}-i^{97}})
Cancel out i^{99}-i^{98} in both numerator and denominator.
Re(-1+\frac{-\left(i^{98}-i^{97}\right)}{i^{98}-i^{97}})
Extract the negative sign in i^{100}-i^{99}.
Re(-1-1)
Cancel out i^{98}-i^{97} in both numerator and denominator.
Re(-2)
Subtract 1 from -1 to get -2.
-2
The real part of -2 is -2.
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}