Evaluate
4-19i
Real Part
4
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5\times 2+5\times \left(-3i\right)-2i\times 2-2\left(-3\right)i^{2}
Multiply complex numbers 5-2i and 2-3i like you multiply binomials.
5\times 2+5\times \left(-3i\right)-2i\times 2-2\left(-3\right)\left(-1\right)
By definition, i^{2} is -1.
10-15i-4i-6
Do the multiplications.
10-6+\left(-15-4\right)i
Combine the real and imaginary parts.
4-19i
Do the additions.
Re(5\times 2+5\times \left(-3i\right)-2i\times 2-2\left(-3\right)i^{2})
Multiply complex numbers 5-2i and 2-3i like you multiply binomials.
Re(5\times 2+5\times \left(-3i\right)-2i\times 2-2\left(-3\right)\left(-1\right))
By definition, i^{2} is -1.
Re(10-15i-4i-6)
Do the multiplications in 5\times 2+5\times \left(-3i\right)-2i\times 2-2\left(-3\right)\left(-1\right).
Re(10-6+\left(-15-4\right)i)
Combine the real and imaginary parts in 10-15i-4i-6.
Re(4-19i)
Do the additions in 10-6+\left(-15-4\right)i.
4
The real part of 4-19i is 4.
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}