Problem 17 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The product of the two given complex numbers in standard form is \(26\).

Step 1: Write Down the Complex Numbers

First, write down the complex numbers being multiplied, namely: \(-5 + i\) and \(-5 - i\).

Step 2: Expand the Product

Next, multiply these two complex numbers, much like binoculars in Algebra. Apply the distributive property while treating 'i' as a variable to get: \((-5 \times -5) + (-5 \times -i) + (i \times -5) + (i \times -i)\). This simplifies to: \(25 + 5i - 5i - i^2)\.

Step 3: Simplify

Now, replace \(i^2\) with -1 and simplify the equation, resulting in \(25 + 1 = 26\).