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Chapter 1: Problem 60

Explain how to multiply complex numbers and give an example.

Short Answer

Expert verified
To multiply two complex numbers \(a + bi\) and \(c + di\), distribute each part of the first complex number to each part of the second, simplify and don't forget that \(i^2 = -1\). For the two complex numbers \(3 + 4i\) and \(1 + 2i\), the product is \(-5 + 10i\).

Step by step solution

01

Understand complex numbers

Complex numbers have a real part and an imaginary part, typically written as \(a + bi\), where \(a\) is the real part and \(b\) is the imaginary part.
02

Multiply complex numbers

When multiplying complex numbers, distribute each part of the first complex number to each part of the second complex number. For instance, given two complex numbers \(a + bi\) and \(c + di\), their product would be \((a + bi) * (c + di) = ac + adi + bci - bd\). And simplifying this expression will yield \(ac - bd + (ad + bc)i\).
03

Give an example

Consider two complex numbers \(3 + 4i\) and \(1 + 2i\). Multiplying them as per the above rules gives \(3*(1) + 3*(2i) + 4i*(1) + 4i*2i = 3 + 6i + 4i - 8 = -5 + 10i\).

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