Evaluate (complex solution)
\frac{\sqrt{5}i}{5}\approx 0.447213595i
Real Part (complex solution)
0
Evaluate
\text{Indeterminate}
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\frac{\sqrt{-1}}{\sqrt{5}}
Rewrite the square root of the division \sqrt{-\frac{1}{5}} as the division of square roots \frac{\sqrt{-1}}{\sqrt{5}}.
\frac{i}{\sqrt{5}}
Calculate the square root of -1 and get i.
\frac{i\sqrt{5}}{\left(\sqrt{5}\right)^{2}}
Rationalize the denominator of \frac{i}{\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.
\frac{i\sqrt{5}}{5}
The square of \sqrt{5} is 5.
\frac{1}{5}i\sqrt{5}
Divide i\sqrt{5} by 5 to get \frac{1}{5}i\sqrt{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}