Skip to main content
Evaluate
Tick mark Image
Real Part
Tick mark Image

Similar Problems from Web Search

Share

\frac{\left(50+5i\right)\left(5+5i\right)}{\left(5-5i\right)\left(5+5i\right)}
Multiply both numerator and denominator by the complex conjugate of the denominator, 5+5i.
\frac{\left(50+5i\right)\left(5+5i\right)}{5^{2}-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{\left(50+5i\right)\left(5+5i\right)}{50}
By definition, i^{2} is -1. Calculate the denominator.
\frac{50\times 5+50\times \left(5i\right)+5i\times 5+5\times 5i^{2}}{50}
Multiply complex numbers 50+5i and 5+5i like you multiply binomials.
\frac{50\times 5+50\times \left(5i\right)+5i\times 5+5\times 5\left(-1\right)}{50}
By definition, i^{2} is -1.
\frac{250+250i+25i-25}{50}
Do the multiplications in 50\times 5+50\times \left(5i\right)+5i\times 5+5\times 5\left(-1\right).
\frac{250-25+\left(250+25\right)i}{50}
Combine the real and imaginary parts in 250+250i+25i-25.
\frac{225+275i}{50}
Do the additions in 250-25+\left(250+25\right)i.
\frac{9}{2}+\frac{11}{2}i
Divide 225+275i by 50 to get \frac{9}{2}+\frac{11}{2}i.
Re(\frac{\left(50+5i\right)\left(5+5i\right)}{\left(5-5i\right)\left(5+5i\right)})
Multiply both numerator and denominator of \frac{50+5i}{5-5i} by the complex conjugate of the denominator, 5+5i.
Re(\frac{\left(50+5i\right)\left(5+5i\right)}{5^{2}-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{\left(50+5i\right)\left(5+5i\right)}{50})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{50\times 5+50\times \left(5i\right)+5i\times 5+5\times 5i^{2}}{50})
Multiply complex numbers 50+5i and 5+5i like you multiply binomials.
Re(\frac{50\times 5+50\times \left(5i\right)+5i\times 5+5\times 5\left(-1\right)}{50})
By definition, i^{2} is -1.
Re(\frac{250+250i+25i-25}{50})
Do the multiplications in 50\times 5+50\times \left(5i\right)+5i\times 5+5\times 5\left(-1\right).
Re(\frac{250-25+\left(250+25\right)i}{50})
Combine the real and imaginary parts in 250+250i+25i-25.
Re(\frac{225+275i}{50})
Do the additions in 250-25+\left(250+25\right)i.
Re(\frac{9}{2}+\frac{11}{2}i)
Divide 225+275i by 50 to get \frac{9}{2}+\frac{11}{2}i.
\frac{9}{2}
The real part of \frac{9}{2}+\frac{11}{2}i is \frac{9}{2}.