Find the product of these complex numbers.(5 + 6i)(3 - 3i) =A.15 - 18iB.-3 + 3iC.15 + 18iD.33 + 3i

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Dan Dinu asked Sep 6, 2023

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Find the product of these complex numbers.(5 + 6i)(3 - 3i) =A.15 - 18iB.-3 + 3iC.15 + 18iD.33 + 3i

Find the product of these complex numbers.(5 + 6i)(3 - 3i) =A.15 - 18iB.-3 + 3iC.15 + 18iD-example-1

Mathematics
college

Dan Dinu asked Sep 6, 2023

by Dan Dinu

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Solution:

To find the product of the complex numbers given:

we multiply the terms in the second parentheses by each term in the first parentheses.

Thus, we have

$\begin{gathered} 5(3-3i)+6i(3-3i) \\ open\text{ parentheses,} \\ 15-15i+18i-18i^2 \\ but \\ i^2=-1 \\ thus, \\ 15-15i+18i-18(-1) \\ =15-15i+18i+18 \\ collect\text{ like terms,} \\ (15+18)+i(18-15) \\ =33+3i \end{gathered}$

Hence, the product is

The correct option is D

Joelgullander answered Sep 12, 2023

by Joelgullander

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