Answered

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What is the product of the complex numbers below?(3 - 2i)(1 + 7i)A.-11 + 19iB.17 + 19iC.-11 - 23iD.17 - 23i

What Is The Product Of The Complex Numbers Below3 2i1 7iA11 19iB17 19iC11 23iD17 23i class=

Sagot :

Solution:

Given:

[tex](3-2i)(1+7i)[/tex]

To find the product, we multiply the terms in the second parentheses by each term in the first parentheses.

Thus, we have

[tex]\begin{gathered} 3(1+7i)-2i(1+7i) \\ open\text{ parentheses,} \\ 3+21i-2i-14i^2 \\ but\text{ i}^2=-1 \\ thus,\text{ we have} \\ 3+21i-2i-14(-1) \\ collect\text{ like terms,} \\ (3+14)+i(21-2) \\ \Rightarrow17+19i \end{gathered}[/tex]

Hence, the product of the complex numbers is

[tex]17+19i[/tex]

The correct option is B

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