/*! 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 36 Perform the indicated operations... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 36

Perform the indicated operations and write the result in standard form. $$ (-2+\sqrt{-11})^{2} $$

Short Answer

Expert verified
The result of squaring this complex number is \(-7 - 4\sqrt{11}i\).

Step by step solution

01

Identify the Imaginary Unit

In the term \(\sqrt{-11}\), the negative sign under the square root indicates we are dealing with an imaginary number. Therefore, we can rewrite the term as \(\sqrt{11}i\) where \(i\) is the imaginary unit with property \(i^{2} = -1\). This makes the entire expression \((-2 + \sqrt{11}i)^{2}\)
02

Square the Complex Number

Squaring a complex number requires us to square each term and twice the product of both terms. Applying the formula \((a + bi)^{2} = a^{2} + 2abi - b^{2}\), we get: \((-2)^{2} + 2(-2)*(\sqrt{11}i) - (\sqrt{11}i)^{2} = 4 -4\sqrt{11}i - 11\)
03

Simplify the Expression

Combine the real and imaginary parts to get the expression in standard form: \(4 - 11 - 4\sqrt{11}i = -7 - 4\sqrt{11}i \).

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

Find all values of \(x\) satisfying the given conditions. $$ \begin{aligned} &y_{1}=-x^{2}+4 x-2, y_{2}=-3 x^{2}+x-1, \text { and } &y_{1}-y_{2}=0 \end{aligned} $$

Find all values of \(x\) satisfying the given conditions. $$ y_{1}=x-1, y_{2}=x+4, \text { and } y_{1} y_{2}=14 $$

Find all values of \(x\) satisfying the given conditions. $$ y=5 x^{2}+3 x \text { and } y=2 $$

List all numbers that must be excluded from the domain of each rational expression. $$ \frac{7}{2 x^{2}-8 x+5} $$

Explaining the Concepts. Explain why \(|x|<-4\) has no solution.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

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.