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Chapter 2: Problem 66

Explain how to multiply complex numbers and give an example.

Short Answer

Expert verified
Therefore, the product of the complex numbers \(3 + 2i\) and \(1 + 4i\) is \(-5 + 14i\).

Step by step solution

01

Write the Complex Numbers

Let's take two complex numbers for our example: \(3 + 2i\) and \(1 + 4i\). Write them in the form \(a + bi\), where \(a\) and \(b\) are real numbers.
02

Distributive Property

Use the Distributive Property to multiply each part of the first complex number by each part of the second complex number. This will give the following: \( (3)(1) + (3)(4i) + (2i)(1) + (2i)(4i) = 3 + 12i + 2i + 8i^2 \).
03

Simplify Expression

As per definition, substitute \(i^2\) with -1 and combine like terms. This results to the following: \( 3 + 12i + 2i - 8 = -5 + 14i \).

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