Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

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College Algebra

1. Equations & Inequalities

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1:05 minutes

Problem 79

Textbook Question

Find each quotient. Write answers in standard form. -5 / i

Verified step by step guidance

Step 1: Recall that the standard form of a complex number is a + bi, where a and b are real numbers. We want to express the given expression in this form.

Step 2: To do this, we need to get rid of the 'i' in the denominator. We can achieve this by multiplying the numerator and denominator by the conjugate of 'i', which is '-i'.

Step 3: Multiply -5 by -i in the numerator to get 5i.

Step 4: Multiply i by -i in the denominator to get -i^2. Remember that i^2 = -1, so -i^2 = 1.

Step 5: Now, the expression is in the form a + bi, where a = 0 and b = 5. So, the quotient in standard form is 0 + 5i or simply 5i.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, typically expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i', which is defined as the square root of -1. Understanding complex numbers is essential for performing operations involving imaginary units, such as division.

Division of Complex Numbers

Dividing complex numbers often involves multiplying the numerator and denominator by the conjugate of the denominator to eliminate the imaginary unit from the denominator. The conjugate of a complex number a + bi is a - bi. This process simplifies the division and allows the result to be expressed in standard form.

Standard Form of Complex Numbers

The standard form of a complex number is a + bi, where 'a' and 'b' are real numbers. When performing operations with complex numbers, it is important to express the final result in this form for clarity and consistency. This involves ensuring that the real and imaginary parts are clearly separated.