Evaluate
\sqrt{2}\left(-1-i\right)+\left(-1+i\right)\approx -2.414213562-0.414213562i
Real Part
-\sqrt{2}-1
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-1+i-\sqrt{2}-\sqrt{2}i
Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.
-1+i-\sqrt{2}-i\sqrt{2}
Multiply -1 and i to get -i.
-1+i+\left(-1-i\right)\sqrt{2}
Combine -\sqrt{2} and -i\sqrt{2} to get \left(-1-i\right)\sqrt{2}.
Examples
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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