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Chapter 1: Problem 16

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

Short Answer

Expert verified
The product (2+7i)(2-7i) in standard form is 53.

Step by step solution

01

Distribute

Firstly, distribute each term in the first complex number (2+7i) with each term in the second complex number (2-7i) separately: \[ (2 * 2) + (2 * -7i) + (7i * 2) + (7i * -7i) = 4 - 14i + 14i - 49i^2 \]
02

Simplify

Secondly, simplify the expression obtained after the distribution: \[ 4 - 49i^2 \]. The term \( - 14i + 14i \) simplify to zero and remember, the square of 'i', \(i^2\), is -1.
03

Final Calculation

Next, substitute \(i^2\) with -1 and do the calculation: \[ 4 - 49(-1) = 4 + 49 = 53 \]

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