/*! 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 35 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 35

Perform the indicated operations and write the result in standard form. $$ (-3-\sqrt{-7})^{2} $$

Short Answer

Expert verified
The result of the operation \((-3-\sqrt{-7})^{2}\) in standard form is \(2 + 6i\sqrt{7}\)

Step by step solution

01

Rewrite the square root

Rewrite \(\sqrt{-7}\) as \(i\sqrt{7}\), so we get \((-3 - i\sqrt{7})^2\)
02

Apply the binomial formula

Apply the binomial formula for \(a = -3\) and \(b = i\sqrt{7}\) to get \((-3)^2 - 2(-3)(i\sqrt{7}) + (i\sqrt{7})^2\) which simplifies to \(9 + 6i\sqrt{7} - 7\)
03

Simplify the final result

Simplify \(9 + 6i\sqrt{7} - 7\) to get \(2 + 6i\sqrt{7}\).
04

Write the result in standard form

The result in standard form for complex numbers is \(2 + 6i\sqrt{7}\).

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

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can check inequalities by substituting 0 for the variable: When 0 belongs to the solution set, I should obtain a true statement, and when 0 does not belong to the solution set, I should obtain a false statement.

A bank offers two checking account plans. Plan A has a base service charge of 4.00 dollar per month plus 10垄 per check. Plan B charges a base service charge of $2.00 per month plus 15垄 per check. a. Write models for the total monthly costs for each plan if x checks are written. b. Use a graphing utility to graph the models in the same [0, 50, 10] by [0, 10, 1] viewing rectangle. c. Use the graphs (and the intersection feature) to determine for what number of checks per month plan A will be better than plan B. d. Verify the result of part (c) algebraically by solving an inequality.

The length of a rectangular sign is 3 feet longer than the width. If the sign's area is 54 square feet, find its length and width.

In Exercises 95鈥�102, use interval notation to represent all values of x satisfying the given conditions. \(y=8-|5 x+3|\) and \(y\) is at least 6

An isosceles right triangle has legs that are the same length and acute angles each measuring \(45^{\circ} .\) a. Write an expression in terms of \(a\) that represents the length of the hypotenuse.\ b. Use your result from part (a) to write a sentence that describes the length of the hypotenuse of an isosceles right triangle in terms of the length of a leg.
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

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.