Evaluate
\left(-\frac{50}{2501}-\frac{2500}{2501}i\right)\lambda +\left(\frac{1}{2501}+\frac{50}{2501}i\right)
Expand
\left(-\frac{50}{2501}-\frac{2500}{2501}i\right)\lambda +\left(\frac{1}{2501}+\frac{50}{2501}i\right)
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\left(-\frac{1}{5}-10i\right)\left(-\frac{5}{2501}\right)+\left(-\frac{1}{5}-10i\right)\times \frac{250}{2501}\lambda
Use the distributive property to multiply -\frac{1}{5}-10i by -\frac{5}{2501}+\frac{250}{2501}\lambda .
-\frac{1}{5}\left(-\frac{5}{2501}\right)-10i\left(-\frac{5}{2501}\right)+\left(-\frac{1}{5}-10i\right)\times \frac{250}{2501}\lambda
Multiply -\frac{1}{5}-10i times -\frac{5}{2501}.
\frac{1}{2501}+\frac{50}{2501}i+\left(-\frac{1}{5}-10i\right)\times \frac{250}{2501}\lambda
Do the multiplications in -\frac{1}{5}\left(-\frac{5}{2501}\right)-10i\left(-\frac{5}{2501}\right).
\frac{1}{2501}+\frac{50}{2501}i+\left(-\frac{1}{5}\times \frac{250}{2501}-10i\times \frac{250}{2501}\right)\lambda
Multiply -\frac{1}{5}-10i times \frac{250}{2501}.
\frac{1}{2501}+\frac{50}{2501}i+\left(-\frac{50}{2501}-\frac{2500}{2501}i\right)\lambda
Do the multiplications in -\frac{1}{5}\times \frac{250}{2501}-10i\times \frac{250}{2501}.
\left(-\frac{1}{5}-10i\right)\left(-\frac{5}{2501}\right)+\left(-\frac{1}{5}-10i\right)\times \frac{250}{2501}\lambda
Use the distributive property to multiply -\frac{1}{5}-10i by -\frac{5}{2501}+\frac{250}{2501}\lambda .
-\frac{1}{5}\left(-\frac{5}{2501}\right)-10i\left(-\frac{5}{2501}\right)+\left(-\frac{1}{5}-10i\right)\times \frac{250}{2501}\lambda
Multiply -\frac{1}{5}-10i times -\frac{5}{2501}.
\frac{1}{2501}+\frac{50}{2501}i+\left(-\frac{1}{5}-10i\right)\times \frac{250}{2501}\lambda
Do the multiplications in -\frac{1}{5}\left(-\frac{5}{2501}\right)-10i\left(-\frac{5}{2501}\right).
\frac{1}{2501}+\frac{50}{2501}i+\left(-\frac{1}{5}\times \frac{250}{2501}-10i\times \frac{250}{2501}\right)\lambda
Multiply -\frac{1}{5}-10i times \frac{250}{2501}.
\frac{1}{2501}+\frac{50}{2501}i+\left(-\frac{50}{2501}-\frac{2500}{2501}i\right)\lambda
Do the multiplications in -\frac{1}{5}\times \frac{250}{2501}-10i\times \frac{250}{2501}.
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