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Chapter 2: Problem 17

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

Short Answer

Expert verified
The product of the complex numbers \(-5 + i\) and \(-5 - i\) is \(24 + 10i\).

Step by step solution

01

Apply the FOIL method

First, multiply the first terms in each binomial, next the outside terms, then the inside terms, and finally the last terms. \[(-5 \cdot -5) + (-5 \cdot -i) + (i \cdot -5) + (i \cdot -i)\]
02

Simplify the resulting terms

Simplify the terms obtained from the FOIL multiplication. Remember that \(i^2 = -1\). So \[(25) + (5i) + (5i) + (-1) = 24 + 10i\]
03

Write the final answer in standard form

The resulting expression, \(24 + 10i\), is already in the standard form \(a + bi\) of a complex number.

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