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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 29a
Capitolo 2, Problema 29a

Simplify and write the result in standard form. √-49

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1
Recognize that the square root of a negative number involves imaginary numbers. The imaginary unit, denoted as 'i', is defined as the square root of -1, i.e., i = √-1.
Rewrite the given expression √-49 as √(-1 × 49).
Use the property of square roots that √(a × b) = √a × √b to separate the terms: √(-1 × 49) = √-1 × √49.
Substitute √-1 with 'i' and simplify √49 to 7 (since 49 is a perfect square): √-1 × √49 = i × 7.
Write the final simplified expression in standard form for complex numbers: 7i.

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Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, 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 simplifying expressions involving square roots of negative numbers.
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Dividing Complex Numbers

Imaginary Unit

The imaginary unit 'i' is defined as the square root of -1. It allows for the extension of the real number system to include solutions to equations that do not have real solutions, such as x^2 + 1 = 0. In the context of the question, √-49 can be rewritten using 'i' to express the result in terms of complex numbers.
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Square Roots of Negative Numbers

Standard Form of Complex Numbers

The standard form of a complex number is a + bi, where 'a' and 'b' are real numbers. When simplifying expressions involving square roots of negative numbers, it is important to express the result in this form to clearly indicate both the real and imaginary components. For example, √-49 simplifies to 7i, which is in standard form.
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Multiplying Complex Numbers
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