/*! 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 84 Simplify the complex number and ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 84

Simplify the complex number and write it in standard form. $$(-i)^{3}$$

Short Answer

Expert verified
The simplified form of \((-i)^3\) is \(i\).

Step by step solution

01

Understanding the imaginary unit \(i\)

First, let's remember what \(i\) represents in complex numbers. In this context, \(i\) is the imaginary unit, which is defined by \(i^2 = -1\). Therefore, \(i^3 = i^2 \cdot i = -i\).
02

Applying properties of exponents

Now, let's apply this concept to the given problem: \((-i)^3\). When -i is raised to the 3rd power, it means \((-i) \cdot (-i) \cdot (-i)\).
03

Simplification

Thus, \((-i)^3=(-i) \cdot (-i) \cdot (-i) = (-1) \cdot i \cdot (-1) \cdot i \cdot (-1) \cdot i = - i \cdot - i \cdot - i = - i^2 \cdot - i = -(-1) \cdot -i = 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 real zeros of the function. $$f(z)=12 z^{3}-4 z^{2}-27 z+9$$

Think About It Let \(y=f(x)\) be a cubic polynomial with leading coefficient \(a=-1\) and \(f(2)=f(i)=0\) Write an equation for \(f\)

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: \(x=-1\)

Prove that the complex conjugate of the product of two complex numbers \(a_{1}+b_{1} i\) and \(a_{2}+b_{2} i\) is the product of their complex conjugates.

Use the given zero to find all the zeros of the function. Function \(h(x)=3 x^{3}-4 x^{2}+8 x+8\) Zero \(1-\sqrt{3} i\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

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.