Evaluate
-\frac{1}{5}-\frac{21}{5}i=-0.2-4.2i
Real Part
-\frac{1}{5} = -0.2
Share
Copied to clipboard
\frac{\left(21-i\right)i}{5i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(21-i\right)i}{-5}
By definition, i^{2} is -1. Calculate the denominator.
\frac{21i-i^{2}}{-5}
Multiply 21-i times i.
\frac{21i-\left(-1\right)}{-5}
By definition, i^{2} is -1.
\frac{1+21i}{-5}
Do the multiplications in 21i-\left(-1\right). Reorder the terms.
-\frac{1}{5}-\frac{21}{5}i
Divide 1+21i by -5 to get -\frac{1}{5}-\frac{21}{5}i.
Re(\frac{\left(21-i\right)i}{5i^{2}})
Multiply both numerator and denominator of \frac{21-i}{5i} by imaginary unit i.
Re(\frac{\left(21-i\right)i}{-5})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{21i-i^{2}}{-5})
Multiply 21-i times i.
Re(\frac{21i-\left(-1\right)}{-5})
By definition, i^{2} is -1.
Re(\frac{1+21i}{-5})
Do the multiplications in 21i-\left(-1\right). Reorder the terms.
Re(-\frac{1}{5}-\frac{21}{5}i)
Divide 1+21i by -5 to get -\frac{1}{5}-\frac{21}{5}i.
-\frac{1}{5}
The real part of -\frac{1}{5}-\frac{21}{5}i is -\frac{1}{5}.
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}