Evaluate
23
Real Part
23
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4^{2}-\left(i\sqrt{7}\right)^{2}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
16-\left(i\sqrt{7}\right)^{2}
Calculate 4 to the power of 2 and get 16.
16-i^{2}\left(\sqrt{7}\right)^{2}
Expand \left(i\sqrt{7}\right)^{2}.
16-\left(-\left(\sqrt{7}\right)^{2}\right)
Calculate i to the power of 2 and get -1.
16-\left(-7\right)
The square of \sqrt{7} is 7.
16+7
The opposite of -7 is 7.
23
Add 16 and 7 to get 23.
Re(4^{2}-\left(i\sqrt{7}\right)^{2})
Consider \left(4+i\sqrt{7}\right)\left(4-i\sqrt{7}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
Re(16-\left(i\sqrt{7}\right)^{2})
Calculate 4 to the power of 2 and get 16.
Re(16-i^{2}\left(\sqrt{7}\right)^{2})
Expand \left(i\sqrt{7}\right)^{2}.
Re(16-\left(-\left(\sqrt{7}\right)^{2}\right))
Calculate i to the power of 2 and get -1.
Re(16-\left(-7\right))
The square of \sqrt{7} is 7.
Re(16+7)
The opposite of -7 is 7.
Re(23)
Add 16 and 7 to get 23.
23
The real part of 23 is 23.
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}