/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 Perform the operation and write ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 37

Perform the operation and write the result in standard form. $$(\sqrt{14}+\sqrt{10} i)(\sqrt{14}-\sqrt{10} i)$$

Short Answer

Expert verified
The result is 4

Step by step solution

01

Identify the Real and Imaginary Part

Both complex numbers consist of a real part and an imaginary part. In this case, \(\sqrt{14}\) is the real part (a) and \(\sqrt{10}\) is the imaginary part (b).
02

Apply the Difference of Squares Formula

The Difference of Squares is a formula that states that \((a+b)(a-b) = a^2 - b^2\). Applying the formula to \((\sqrt{14}+\sqrt{10}i)(\sqrt{14}-\sqrt{10}i)\), where a is \(\sqrt{14}\) and b is \(\sqrt{10}\), it simplifies to \(a^2 - b^2\), or \((\sqrt{14})^2 - (\sqrt{10})^2\).
03

Evaluate the Squares

Squaring the square roots \((\sqrt{14})^2\) and \((\sqrt{10})^2\), we get 14 and 10 respectively.
04

Subtract the Squares

The subtraction gives the result \(14 - 10\).
05

Compute the Result

After subtracting the squares, we obtain the result 4, which is the final answer.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write the polynomial as the product of linear factors and list all the zeros of the function. $$h(x)=x^{3}-x+6$$

Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=5 x^{3}-9 x^{2}+28 x+6$$

Find the rational zeros of the polynomial function. $$f(z)=z^{3}+\frac{11}{6} z^{2}-\frac{1}{2} z-\frac{1}{3}=\frac{1}{6}\left(6 z^{3}+11 z^{2}-3 z-2\right)$$

Use synthetic division to verify the upper and lower bounds of the real zeros of \(f\) \(f(x)=x^{3}-4 x^{2}+1\) (a) Upper: \(x=4\) (b) Lower: \(x=-1\)

Use synthetic division to verify the upper and lower bounds of the real zeros of \(f\) \(f(x)=2 x^{4}-8 x+3\) (a) Upper: \(x=3\) (b) Lower: \(x=-4\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.