Evaluate
-4-2i
Real Part
-4
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\frac{1-9i+\left(3+i\right)}{2i}
Calculate the square root of 8+6i and get 3+i.
\frac{1+3+\left(-9+1\right)i}{2i}
Combine the real and imaginary parts in numbers 1-9i and 3+i.
\frac{4-8i}{2i}
Add 1 to 3. Add -9 to 1.
\frac{\left(4-8i\right)i}{2i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(4-8i\right)i}{-2}
By definition, i^{2} is -1. Calculate the denominator.
\frac{4i-8i^{2}}{-2}
Multiply 4-8i times i.
\frac{4i-8\left(-1\right)}{-2}
By definition, i^{2} is -1.
\frac{8+4i}{-2}
Do the multiplications in 4i-8\left(-1\right). Reorder the terms.
-4-2i
Divide 8+4i by -2 to get -4-2i.
Re(\frac{1-9i+\left(3+i\right)}{2i})
Calculate the square root of 8+6i and get 3+i.
Re(\frac{1+3+\left(-9+1\right)i}{2i})
Combine the real and imaginary parts in numbers 1-9i and 3+i.
Re(\frac{4-8i}{2i})
Add 1 to 3. Add -9 to 1.
Re(\frac{\left(4-8i\right)i}{2i^{2}})
Multiply both numerator and denominator of \frac{4-8i}{2i} by imaginary unit i.
Re(\frac{\left(4-8i\right)i}{-2})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{4i-8i^{2}}{-2})
Multiply 4-8i times i.
Re(\frac{4i-8\left(-1\right)}{-2})
By definition, i^{2} is -1.
Re(\frac{8+4i}{-2})
Do the multiplications in 4i-8\left(-1\right). Reorder the terms.
Re(-4-2i)
Divide 8+4i by -2 to get -4-2i.
-4
The real part of -4-2i is -4.
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}