Chapter 4.5, Problem 66STP

To determine

To find: the value of b from the complex root where a and b are real numbers.

Answer to Problem 66STP

The value of $\text{b=34}$ .

Explanation of Solution

Given:

  $\text{5+3i}$ .

Concept used:

In order to rationalize the denominator, it need to get rid of all radicals that are in the denominator.

Step 1: multiply the numerator and denominator by a radical that will get ride of the radical in the denominator.

Step2: make sure all radicals are simplified.

Step 3: Simplify the fraction if needed.

Calculation:

It has to be second complex conjugate root:

  $\text{5+3i}$ .

Product root here is $\text{1}\times \text{b=b}$ and product of the root is equal to $\text{b}$ .

  $\left(\text{5-3i}\right)\times \left(\text{5+3i}\right)\text{=b}$ .

  $\Rightarrow {\text{25-9i}}^2$ .

Since ${\text{i}}^{\text{2}}=-1$ :

  $\Rightarrow \text{25+9=34}\text{.}$

Hence the value of $\text{b=34}$ .