Evaluate
-\frac{5}{2}-2i=-2.5-2i
Real Part
-\frac{5}{2} = -2\frac{1}{2} = -2.5
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\frac{\left(4-5i\right)i}{2i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(4-5i\right)i}{-2}
By definition, i^{2} is -1. Calculate the denominator.
\frac{4i-5i^{2}}{-2}
Multiply 4-5i times i.
\frac{4i-5\left(-1\right)}{-2}
By definition, i^{2} is -1.
\frac{5+4i}{-2}
Do the multiplications in 4i-5\left(-1\right). Reorder the terms.
-\frac{5}{2}-2i
Divide 5+4i by -2 to get -\frac{5}{2}-2i.
Re(\frac{\left(4-5i\right)i}{2i^{2}})
Multiply both numerator and denominator of \frac{4-5i}{2i} by imaginary unit i.
Re(\frac{\left(4-5i\right)i}{-2})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{4i-5i^{2}}{-2})
Multiply 4-5i times i.
Re(\frac{4i-5\left(-1\right)}{-2})
By definition, i^{2} is -1.
Re(\frac{5+4i}{-2})
Do the multiplications in 4i-5\left(-1\right). Reorder the terms.
Re(-\frac{5}{2}-2i)
Divide 5+4i by -2 to get -\frac{5}{2}-2i.
-\frac{5}{2}
The real part of -\frac{5}{2}-2i is -\frac{5}{2}.
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\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}