Evaluate
1-3i
Real Part
1
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1\times 2+1\left(-i\right)-i\times 2-\left(-i^{2}\right)
Multiply complex numbers 1-i and 2-i like you multiply binomials.
1\times 2+1\left(-i\right)-i\times 2-\left(-\left(-1\right)\right)
By definition, i^{2} is -1.
2-i-2i-1
Do the multiplications.
2-1+\left(-1-2\right)i
Combine the real and imaginary parts.
1-3i
Do the additions.
Re(1\times 2+1\left(-i\right)-i\times 2-\left(-i^{2}\right))
Multiply complex numbers 1-i and 2-i like you multiply binomials.
Re(1\times 2+1\left(-i\right)-i\times 2-\left(-\left(-1\right)\right))
By definition, i^{2} is -1.
Re(2-i-2i-1)
Do the multiplications in 1\times 2+1\left(-i\right)-i\times 2-\left(-\left(-1\right)\right).
Re(2-1+\left(-1-2\right)i)
Combine the real and imaginary parts in 2-i-2i-1.
Re(1-3i)
Do the additions in 2-1+\left(-1-2\right)i.
1
The real part of 1-3i is 1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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y = 3x + 4
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Matrix
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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}