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Chapter 2: Problem 15

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

Short Answer

Expert verified
The product of the complex numbers (3+5 i) and (3-5 i) in standard form is 34

Step by step solution

01

Apply the distributive property

To do this, multiply each part of the first complex number by each part of the second complex number. In other words, apply the FOIL method - first, outer, inner and last. This gives you \((3 * 3)+(3 * -5 i)+(5 i * 3)+(5 i * -5 i)\)
02

Evaluate each multiplication

Upon breaking it down we get \(9 - 15i + 15i - 25i^2\)
03

Remember that \(i^2\) is -1

Keep in mind that \(i^2\) is -1. Substituting -1 for \(i^2\) in our equation gives us \(9 - 25*(-1)= 9 + 25\)
04

Simplify the expression

Add together the real parts to simplify the expression. This should give us a final answer of 34

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Most popular questions from this chapter

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The graph of a rational function can never cross a vertical asymptote.

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