Evaluate
2+3i
Real Part
2
Share
Copied to clipboard
\frac{6i^{2}+10+19i}{5+2i}
Do the additions in 10+4i+15i.
\frac{6\left(-1\right)+10+19i}{5+2i}
Calculate i to the power of 2 and get -1.
\frac{-6+10+19i}{5+2i}
Multiply 6 and -1 to get -6.
\frac{4+19i}{5+2i}
Do the additions in -6+10+19i.
\frac{\left(4+19i\right)\left(5-2i\right)}{\left(5+2i\right)\left(5-2i\right)}
Multiply both numerator and denominator by the complex conjugate of the denominator, 5-2i.
\frac{58+87i}{29}
Do the multiplications in \frac{\left(4+19i\right)\left(5-2i\right)}{\left(5+2i\right)\left(5-2i\right)}.
2+3i
Divide 58+87i by 29 to get 2+3i.
Re(\frac{6i^{2}+10+19i}{5+2i})
Do the additions in 10+4i+15i.
Re(\frac{6\left(-1\right)+10+19i}{5+2i})
Calculate i to the power of 2 and get -1.
Re(\frac{-6+10+19i}{5+2i})
Multiply 6 and -1 to get -6.
Re(\frac{4+19i}{5+2i})
Do the additions in -6+10+19i.
Re(\frac{\left(4+19i\right)\left(5-2i\right)}{\left(5+2i\right)\left(5-2i\right)})
Multiply both numerator and denominator of \frac{4+19i}{5+2i} by the complex conjugate of the denominator, 5-2i.
Re(\frac{58+87i}{29})
Do the multiplications in \frac{\left(4+19i\right)\left(5-2i\right)}{\left(5+2i\right)\left(5-2i\right)}.
Re(2+3i)
Divide 58+87i by 29 to get 2+3i.
2
The real part of 2+3i is 2.
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}