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Chapter 1: Problem 13

Find each product and write the result in standard form. $$ (7-5 i)(-2-3 i) $$

Short Answer

Expert verified
The product of \( (7-5i) \) and \( (-2-3i) \) is \( 1-11i \)

Step by step solution

01

Distribute the terms

First, distribute both terms in \( (7-5i) \) to each term in \( (-2-3i) \). This gives: \( (7)(-2) + (7)(-3i) - (5i)(-2) - (5i)(-3i) \)
02

Simplify the terms

Next, simplify each of the terms, using the fact that \( i^{2} = -1 \): \( -14 - 21i +10i -15i^{2} \).
03

Combine like terms

Combine the real and imaginary terms: \( -14 - 11i -15(-1) \).
04

Simplify the expression

Now use the fact that \( i^{2} = -1 \) to simplify our expression to its final form: \( -14 + 15 - 11i = 1 - 11i \).

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