Question 1209237
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I'll provide a similar example.


Let's say we want to evaluate (7-5i)*(4+9i)


I'll use the <a href="https://www.algebra.com/algebra/homework/playground/lessons/box-method.lesson">box method</a>.


Write the terms 7 and -5i along the left side
Write the terms 4 and 9i along the top row
<table border = "1" cellpadding = "5"><tr><td></td><td>4</td><td>9i</td></tr><tr><td>7</td><td></td><td></td></tr><tr><td>-5i</td><td></td><td></td></tr></table>


To fill the four inner cells, we multiply the headers.
Example: -5i*9i = -45i^2 = -45*(-1) = 45 is in the bottom right corner.
<table border = "1" cellpadding = "5"><tr><td></td><td>4</td><td>9i</td></tr><tr><td>7</td><td>28</td><td>63i</td></tr><tr><td>-5i</td><td>-20i</td><td>45</td></tr></table>


Terms along the northwest diagonal are the real components.
So 28+45 = 73 is the real part of the computation.


Meanwhile, terms along the northeast diagonal are the imaginary components.
-20i+63i = 43i


We determine that
(7-5i)*(4+9i) = 73+43i
Verification using <a href="https://www.wolframalpha.com/input?i=%287-5i%29*%284%2B9i%29+%3D+73+%2B+43i">WolframAlpha</a>


The general template for multiplying two complex numbers is
(a+bi)*(c+di) = (ac - bd) + (bc + ad)*i


Another approach you could use is the FOIL method.
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