Evaluate
7+40i
Real Part
7
Share
Copied to clipboard
-9-\left(-4i\right)+4i\times 9+4\left(-4\right)i^{2}
Multiply complex numbers -1+4i and 9-4i like you multiply binomials.
-9-\left(-4i\right)+4i\times 9+4\left(-4\right)\left(-1\right)
By definition, i^{2} is -1.
-9+4i+36i+16
Do the multiplications.
-9+16+\left(4+36\right)i
Combine the real and imaginary parts.
7+40i
Do the additions.
Re(-9-\left(-4i\right)+4i\times 9+4\left(-4\right)i^{2})
Multiply complex numbers -1+4i and 9-4i like you multiply binomials.
Re(-9-\left(-4i\right)+4i\times 9+4\left(-4\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-9+4i+36i+16)
Do the multiplications in -9-\left(-4i\right)+4i\times 9+4\left(-4\right)\left(-1\right).
Re(-9+16+\left(4+36\right)i)
Combine the real and imaginary parts in -9+4i+36i+16.
Re(7+40i)
Do the additions in -9+16+\left(4+36\right)i.
7
The real part of 7+40i is 7.
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}