Evaluate
\left(-7+\sqrt{2}i\right)\left(-\sqrt{5}i+3\right)\approx -17.83772234+19.89511653i
Real Part
\sqrt{10} - 21 = -17.83772234
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-7\left(3-i\sqrt{5}\right)+i\sqrt{2}\left(3-i\sqrt{5}\right)
Use the distributive property to multiply -7+i\sqrt{2} by 3-i\sqrt{5}.
-21+7i\sqrt{5}+i\sqrt{2}\left(3-i\sqrt{5}\right)
Use the distributive property to multiply -7 by 3-i\sqrt{5}.
-21+7i\sqrt{5}+3i\sqrt{2}+\sqrt{2}\sqrt{5}
Use the distributive property to multiply i\sqrt{2} by 3-i\sqrt{5}.
-21+7i\sqrt{5}+3i\sqrt{2}+\sqrt{10}
To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.
Examples
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{ 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}