Question

For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi. $$ \left(b+\frac{1}{3}\right)^{2}=\frac{4}{9} $$

Name: Problem 31, Chapter 8: Intermediate Algebra for College Students
Uploaded: 2020-06-07T23:22:10-08:00
Duration: 57 s
Channel: Amy Jiang
Description: For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a ±bi. (b+(1)/(3))^2=(4)/(9)

   For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi.
$$
\left(b+\frac{1}{3}\right)^{2}=\frac{4}{9}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 8, Problem 31

Instant Answer

Solved by Expert Amy Jiang

06/07/2020

Step 1

Step 1: Rewrite the equation We can rewrite the equation as: $$ \left(b+\frac{1}{3}\right)^{2}-\frac{4}{9}=0 $$ Show more…

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For Exercises 11-38, use the square root property to solve each equation. Write complex number solutions in the form a $\pm$ bi. $$ \left(b+\frac{1}{3}\right)^{2}=\frac{4}{9} $$

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Key Concepts

Square Root Property

The square root property is a method used to solve equations where a variable expression is squared. To apply this property, take the square root of both sides of the equation, remembering that there are two potential solutions: one positive and one negative, since both squares yield the same result. This property is particularly useful for solving quadratic equations that are in the form (expression)^2 = constant.

Complex Numbers in Standard Form

Complex numbers are numbers that include a real part and an imaginary part, and they are conventionally written in the form a ± bi. Here, 'a' represents the real component, while 'b' is the coefficient of the imaginary part 'i', where i is defined by the property i^2 = -1. When solving equations that lead to complex solutions, it is important to express the answer in this standard form to clearly indicate the real and imaginary parts.

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