Evaluate
\frac{24}{25}+\frac{7}{25}i=0.96+0.28i
Real Part
\frac{24}{25} = 0.96
Share
Copied to clipboard
\frac{\left(7+i\right)\left(7+i\right)}{\left(7-i\right)\left(7+i\right)}
Multiply both numerator and denominator by the complex conjugate of the denominator, 7+i.
\frac{\left(7+i\right)\left(7+i\right)}{7^{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{\left(7+i\right)\left(7+i\right)}{50}
By definition, i^{2} is -1. Calculate the denominator.
\frac{7\times 7+7i+7i+i^{2}}{50}
Multiply complex numbers 7+i and 7+i like you multiply binomials.
\frac{7\times 7+7i+7i-1}{50}
By definition, i^{2} is -1.
\frac{49+7i+7i-1}{50}
Do the multiplications in 7\times 7+7i+7i-1.
\frac{49-1+\left(7+7\right)i}{50}
Combine the real and imaginary parts in 49+7i+7i-1.
\frac{48+14i}{50}
Do the additions in 49-1+\left(7+7\right)i.
\frac{24}{25}+\frac{7}{25}i
Divide 48+14i by 50 to get \frac{24}{25}+\frac{7}{25}i.
Re(\frac{\left(7+i\right)\left(7+i\right)}{\left(7-i\right)\left(7+i\right)})
Multiply both numerator and denominator of \frac{7+i}{7-i} by the complex conjugate of the denominator, 7+i.
Re(\frac{\left(7+i\right)\left(7+i\right)}{7^{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{\left(7+i\right)\left(7+i\right)}{50})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{7\times 7+7i+7i+i^{2}}{50})
Multiply complex numbers 7+i and 7+i like you multiply binomials.
Re(\frac{7\times 7+7i+7i-1}{50})
By definition, i^{2} is -1.
Re(\frac{49+7i+7i-1}{50})
Do the multiplications in 7\times 7+7i+7i-1.
Re(\frac{49-1+\left(7+7\right)i}{50})
Combine the real and imaginary parts in 49+7i+7i-1.
Re(\frac{48+14i}{50})
Do the additions in 49-1+\left(7+7\right)i.
Re(\frac{24}{25}+\frac{7}{25}i)
Divide 48+14i by 50 to get \frac{24}{25}+\frac{7}{25}i.
\frac{24}{25}
The real part of \frac{24}{25}+\frac{7}{25}i is \frac{24}{25}.
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}