I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 1.7 : Complex Numbers
7. Perform the indicated operation and write your answer in standard form.
\[\frac{{7 - i}}{{2 + 10i}}\]Show All Steps Hide All Steps
Because standard form does not allow for \(i\)’s to be in the denominator we’ll need to multiply the numerator and denominator by the conjugate of the denominator, which is \(2 - 10i\).
Show Step 2Multiplying by the conjugate gives,
\[\frac{{7 - i}}{{2 + 10i}}\,\,\frac{{2 - 10i}}{{2 - 10i}} = \frac{{\left( {7 - i} \right)\left( {2 - 10i} \right)}}{{\left( {2 + 10i} \right)\left( {2 - 10i} \right)}}\] Show Step 3Now all we need to do is do the multiplication in the numerator and denominator and put the result in standard form.
\[\frac{{7 - i}}{{2 + 10i}} = \frac{{14 - 72i + 10{i^2}}}{{4 - 100{i^2}}} = \frac{{4 - 72i}}{{104}} = \frac{4}{{104}} - \frac{{72}}{{104}}i = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{1}{{26}} - \frac{9}{{13}}i}}\]