Evaluate
25+46i
Real Part
25
Share
Copied to clipboard
6i-5i\left(-8+5i\right)
Multiply 2 and 3i to get 6i.
6i-\left(5i\left(-8\right)+5\times 5i^{2}\right)
Multiply 5i times -8+5i.
6i-\left(5i\left(-8\right)+5\times 5\left(-1\right)\right)
By definition, i^{2} is -1.
6i-\left(-25-40i\right)
Do the multiplications in 5i\left(-8\right)+5\times 5\left(-1\right). Reorder the terms.
6i+\left(25+40i\right)
The opposite of -25-40i is 25+40i.
25+\left(6+40\right)i
Combine the real and imaginary parts in numbers 6i and 25+40i.
25+46i
Add 6 to 40.
Re(6i-5i\left(-8+5i\right))
Multiply 2 and 3i to get 6i.
Re(6i-\left(5i\left(-8\right)+5\times 5i^{2}\right))
Multiply 5i times -8+5i.
Re(6i-\left(5i\left(-8\right)+5\times 5\left(-1\right)\right))
By definition, i^{2} is -1.
Re(6i-\left(-25-40i\right))
Do the multiplications in 5i\left(-8\right)+5\times 5\left(-1\right). Reorder the terms.
Re(6i+\left(25+40i\right))
The opposite of -25-40i is 25+40i.
Re(25+\left(6+40\right)i)
Combine the real and imaginary parts in numbers 6i and 25+40i.
Re(25+46i)
Add 6 to 40.
25
The real part of 25+46i is 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}