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1. Equations & Inequalities

The Imaginary Unit

1. Equations & Inequalities

The Imaginary Unit

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Square Roots of Negative Numbers

Square Roots of Negative Numbers

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Simplifying Negative Radicals

Simplifying Negative Radicals

Imaginary roots of negative numbers | Imaginary and complex numbers

Imaginary roots of negative numbers | Imaginary and complex numbers

Practice this topic

Multiple Choice

Simplify the given square root. $\sqrt{-75}$

Textbook Question

In Exercises 9–20, find each product and write the result in standard form. (- 5 + 4i)(3 + i)

Textbook Question

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) -6 -2i

Textbook Question

Perform each operation. Write answers in standard form. (6-i) + (7-2i)

Textbook Question

In Exercises 21–28, divide and express the result in standard form. 2/(3 - i)

Textbook Question

Write each number as the product of a real number and i. -√-18

Textbook Question

In Exercises 29–36, simplify and write the result in standard form. √-49

Textbook Question

Simplify each power of i. i^11

Textbook Question

Find each product or quotient. Simplify the answers. √-6 * √-2 / √3

Textbook Question

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 2 + √-4)^2

Textbook Question

Find each sum or difference. Write answers in standard form. (-3+2i) - (-4+2i)

Textbook Question

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^31

Textbook Question

In Exercises 48–57, perform the indicated operations and write the result in standard form. √ (-32) - √ (-18)

Textbook Question

Find each product. Write answers in standard form. (2+i)²

Textbook Question

In Exercises 61–64, write each complex number in standard form. (2 + 3i)^3

Textbook Question

Find each product. Write answers in standard form. 3i(2-i)²

Textbook Question

Evaluate x^2 - 2x + 2 for x = 1 + i.

Textbook Question

Find each quotient. Write answers in standard form. 2 / 3i

Textbook Question

Simplify each power of i. i^-13

Textbook Question

In Exercises 95–99, perform the indicated operations and write the result in standard form. (i^98 - i^94)/i^49

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