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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q 433. (page 844)

In the following exercise, multiply.
$(4 + 3 i) (- 5 + 6 i)$

Short Answer

Expert verified

Value of the expression $(4 + 3 i) (- 5 + 6 i)$ is $- 38 + 9 i$ .

Step by step solution

01

Step 1. Given information.

An expression is $(4 + 3 i) (- 5 + 6 i)$ .

02

Step 2. Multiply the complex numbers.

Use the distributive property:

Thus,

$(4 + 3 i) (- 5 + 6 i) = 4 (- 5 + 6 i) + 3 i (- 5 + 6 i)$

03

Step 3. Simplify and calculate.

Apply the distributive property again.

$\begin{array}{rcl} 4 (- 5 + 6 i) + 3 i (- 5 + 6 i) & = & - 20 + 24 i - 15 i + 18 i^{2} \\ = & - 20 + 24 i - 15 i - 18 \\ = & (- 20 - 18) + (24 i - 15 i) \\ = & - 38 + 9 i \end{array}$

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