Evaluate
4+20i
Real Part
4
Share
Copied to clipboard
\frac{104i\left(5-i\right)}{\left(5+i\right)\left(5-i\right)}
Multiply both numerator and denominator by the complex conjugate of the denominator, 5-i.
\frac{104i\left(5-i\right)}{5^{2}-i^{2}}
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{104i\left(5-i\right)}{26}
By definition, i^{2} is -1. Calculate the denominator.
\frac{104i\times 5+104\left(-1\right)i^{2}}{26}
Multiply 104i times 5-i.
\frac{104i\times 5+104\left(-1\right)\left(-1\right)}{26}
By definition, i^{2} is -1.
\frac{104+520i}{26}
Do the multiplications in 104i\times 5+104\left(-1\right)\left(-1\right). Reorder the terms.
4+20i
Divide 104+520i by 26 to get 4+20i.
Re(\frac{104i\left(5-i\right)}{\left(5+i\right)\left(5-i\right)})
Multiply both numerator and denominator of \frac{104i}{5+i} by the complex conjugate of the denominator, 5-i.
Re(\frac{104i\left(5-i\right)}{5^{2}-i^{2}})
Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
Re(\frac{104i\left(5-i\right)}{26})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{104i\times 5+104\left(-1\right)i^{2}}{26})
Multiply 104i times 5-i.
Re(\frac{104i\times 5+104\left(-1\right)\left(-1\right)}{26})
By definition, i^{2} is -1.
Re(\frac{104+520i}{26})
Do the multiplications in 104i\times 5+104\left(-1\right)\left(-1\right). Reorder the terms.
Re(4+20i)
Divide 104+520i by 26 to get 4+20i.
4
The real part of 4+20i 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}