Evaluate
5-37i
Real Part
5
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5\times 4+5\times \left(-5i\right)-3i\times 4-3\left(-5\right)i^{2}
Multiply complex numbers 5-3i and 4-5i like you multiply binomials.
5\times 4+5\times \left(-5i\right)-3i\times 4-3\left(-5\right)\left(-1\right)
By definition, i^{2} is -1.
20-25i-12i-15
Do the multiplications.
20-15+\left(-25-12\right)i
Combine the real and imaginary parts.
5-37i
Do the additions.
Re(5\times 4+5\times \left(-5i\right)-3i\times 4-3\left(-5\right)i^{2})
Multiply complex numbers 5-3i and 4-5i like you multiply binomials.
Re(5\times 4+5\times \left(-5i\right)-3i\times 4-3\left(-5\right)\left(-1\right))
By definition, i^{2} is -1.
Re(20-25i-12i-15)
Do the multiplications in 5\times 4+5\times \left(-5i\right)-3i\times 4-3\left(-5\right)\left(-1\right).
Re(20-15+\left(-25-12\right)i)
Combine the real and imaginary parts in 20-25i-12i-15.
Re(5-37i)
Do the additions in 20-15+\left(-25-12\right)i.
5
The real part of 5-37i is 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}