Evaluate
-\frac{10}{9}+\frac{2}{3}i\approx -1.111111111+0.666666667i
Real Part
-\frac{10}{9} = -1\frac{1}{9} = -1.1111111111111112
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\frac{\left(-6-10i\right)i}{9i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(-6-10i\right)i}{-9}
By definition, i^{2} is -1. Calculate the denominator.
\frac{-6i-10i^{2}}{-9}
Multiply -6-10i times i.
\frac{-6i-10\left(-1\right)}{-9}
By definition, i^{2} is -1.
\frac{10-6i}{-9}
Do the multiplications in -6i-10\left(-1\right). Reorder the terms.
-\frac{10}{9}+\frac{2}{3}i
Divide 10-6i by -9 to get -\frac{10}{9}+\frac{2}{3}i.
Re(\frac{\left(-6-10i\right)i}{9i^{2}})
Multiply both numerator and denominator of \frac{-6-10i}{9i} by imaginary unit i.
Re(\frac{\left(-6-10i\right)i}{-9})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{-6i-10i^{2}}{-9})
Multiply -6-10i times i.
Re(\frac{-6i-10\left(-1\right)}{-9})
By definition, i^{2} is -1.
Re(\frac{10-6i}{-9})
Do the multiplications in -6i-10\left(-1\right). Reorder the terms.
Re(-\frac{10}{9}+\frac{2}{3}i)
Divide 10-6i by -9 to get -\frac{10}{9}+\frac{2}{3}i.
-\frac{10}{9}
The real part of -\frac{10}{9}+\frac{2}{3}i is -\frac{10}{9}.
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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}