2. Equations and Inequalities

Add and Subtract Complex Numbers

Complex Numbers

Adding and Subtracting Complex (Imaginary) Numbers

In Exercises 95–99, perform the indicated operations and write the result in standard form.

(1 + i)/(1 + 2i) + (1 - i)/(1 - 2i)

Complex Numbers:  Multiplying - Ex 2

Complex Numbers: Multiplying and Dividing in Polar Form, Ex 2

In Exercises 9–20, find each product and write the result in standard form.

(7 - 5i)(- 2 - 3i)

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

Pre-Calculus - Simplify powers of i

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

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √24

Subtract complex numbers: combining like terms

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

In Exercises 37–52, perform the indicated operations and write the result in standard form.

√-64 - √-25

In Exercises 9–20, find each product and write the result in standard form.

(5 - 2i)^2

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

√-108

In Exercises 48–57, perform the indicated operations and write the result in standard form. 6/(5+i)

In Exercises 37–52, perform the indicated operations and write the result in standard form.

(3√-5)(- 4√-12)

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

√-49

In Exercises 1–8, add or subtract as indicated and write the result in standard form.

6 - (- 5 + 4i) - (- 13 - i)

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

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

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

i^135

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) 0

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form.

(2 - 3i)(1 - i) - (3 - i)(3 + i)

Find each quotient. Write answers in standard form. 1-3i / 1+i

Complex Numbers: Dividing - Ex 2

Simplify positive integer powers of i

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

Decide whether each statement is true or false. If false, correct the right side of the equation. (-2+7i) - (10-6i)= -12+i

In Exercises 37–52, perform the indicated operations and write the result in standard form.

(- 3 - √-7)^2

Decide whether each statement is true or false. If false, correct the right side of the equation. √-25 = 5i

Write each number as the product of a real number and i. √-288

Find each product. Write answers in standard form. i(3-4i)(3+4i)

In Exercises 61–64, write each complex number in standard form.

(1 - i)^3

In Exercises 9–20, find each product and write the result in standard form.

- 3i(7i - 5)

Complex Numbers: Operations, Complex Conjugates, and the Linear Factorization Theorem

In Exercises 95–99, perform the indicated operations and write the result in standard form.

(i^85 - i^83)/i^45

In Exercises 61–64, write each complex number in standard form.

(1 + i)^3

In Exercises 61–64, write each complex number in standard form.

(2 + 3i)^3

In Exercises 21–28, divide and express the result in standard form.

(2 + 3i)/(2 + i)

Find each product. Write answers in standard form. (3-i)(3+1)(2-6i)

In Exercises 21–28, divide and express the result in standard form.

5i/(2 - i)

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

i^114

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) -7i

Add complex numbers by combining like terms

Find each quotient. Write answers in standard form. 8 / -i

Perform each operation. Write answers in standard form. -12 -i / -2 -5i

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

i^44

Find each product. Write answers in standard form. (1+3i)(2-5i)

In Exercises 95–99, perform the indicated operations and write the result in standard form.

4/(2 + i)(3 - i)

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

√(1^2 - 4 × 0.5 × 5)

In Exercises 21–28, divide and express the result in standard form.

2/(3 - i)

In Exercises 95–99, perform the indicated operations and write the result in standard form.

(i^98 - i^94)/i^49

Rewriting Powers of  ' i  '  - Ex 1

Complex Numbers - Multiplying and Dividing

Find each product or quotient. Simplify the answers. √-10 / √-40

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

Perform each operation. Write answers in standard form. (5-11i)(5+11i)

Perform Operations with Square Roots of Negative Numbers

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

In Exercises 9–20, find each product and write the result in standard form.

(3 + 5i)(3 - 5i)

Operations with Square Roots with Negative Numbers in the Radicand

Write each number as the product of a real number and i. √-10

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

Find each product. Write answers in standard form. (√6+i)(√6-i)

Work each problem. Show that -3+4i is a solution of the equation x²+6x+25=0.

Find each sum or difference. Write answers in standard form. 3√7 - (4√7-i) -4i + (-2√7+5i)

Write each number in standard form a+bi. -6-√-24 / 2

In Exercises 1–8, add or subtract as indicated and write the result in standard form.

(3 + 2i) - (5 - 7i)

Find each product or quotient. Simplify the answers. √-13 * √-13

In Exercises 48–57, perform the indicated operations and write the result in standard form. (7-i)(2+3i)

In Exercises 21–28, divide and express the result in standard form.

- 6i/(3 + 2i)

Complex Numbers:  Multiplying - Ex 1

Complex Numbers: Multiplying and Dividing in Polar Form, Ex 1

Write each number in standard form a+bi. -3+ √-18 / 24

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form.

(4 - i)^2 - (1 + 2i)^2

Find each sum or difference. Write answers in standard form. (-4-i) - (2+3i) + (-4+5i)

In Exercises 9–20, find each product and write the result in standard form.

(2 + 3i)^2

In Exercises 21–28, divide and express the result in standard form.

8i/(4 - 3i)

Find each product. Write answers in standard form. i(2+7i)(2-7i)

In Exercises 1–8, add or subtract as indicated and write the result in standard form.

(7 + 2i) + (1 - 4i)

Simplifying Negative Radicals

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form.

(2 + i)^2 - (3 - i)^2

Find each product or quotient. Simplify the answers. √-3 * √-8

Multiplying square roots of negative numbers

Perform each operation. Write answers in standard form. (-8+2i)(-1+i)

Write each number as the product of a real number and i. √-25

Complex Numbers: Dividing - Ex 1

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

Multiply complex numbers

In Exercises 37–52, perform the indicated operations and write the result in standard form.

5√-16 + 3√-81

Multiply two complex numbers

In Exercises 9–20, find each product and write the result in standard form.

(- 5 + 4i)(3 + i)

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

Perform each operation. Write answers in standard form. 15i- (3+2i) -11

Work each problem. Show that √2/2 + √2/2 i is a square root of i.

Decide whether each statement is true or false. If false, correct the right side of the equation. i^12 = 1

Simplifying a power of i

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form.

5√-16 + 3√-81

In Exercises 37–52, perform the indicated operations and write the result in standard form.

(- 2 + √-4)^2

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

Rewriting Powers of  ' i  '  - Ex 2

Write each number in standard form a+bi. 10+ √-200 / 5

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form.

(8 + 9i)(2 - i) - (1 - i)(1 + i)

In Exercises 9–20, find each product and write the result in standard form.

(- 5 + i)(- 5 - i)

In Exercises 95–99, perform the indicated operations and write the result in standard form.

8/(1 + 2/i)

Complex Numbers: Dividing - Ex 3

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

Find each product or quotient. Simplify the answers. √-30 / √-10

In Exercises 37–52, perform the indicated operations and write the result in standard form.

(- 6 - √-12)/48

Complex Numbers - Graphing, Adding, Subtracting

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

√(3^2 - 4 × 2 × 5)

In Exercises 21–28, divide and express the result in standard form.

2i/(1 + i)

Imaginary roots of negative numbers | Imaginary and complex numbers

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

i^31

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

Find each sum or difference. Write answers in standard form. (3+2i) + (9+3i)

Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptions will apply.) √-36

Rationalize Denominator with Imaginary Part in Complex Number

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

In Exercises 1–8, add or subtract as indicated and write the result in standard form.

8i - (14 - 9i)

Subtract complex numbers

Evaluate higher powers of i

Perform each operation. Write answers in standard form. -5i(3-i)²

Find each product or quotient. Simplify the answers. √-24 / √8

In Exercises 37–52, perform the indicated operations and write the result in standard form.

(- 8 + √-32)/24

In Exercises 37–52, perform the indicated operations and write the result in standard form.

√-8 (√-3 - √5)

Use imaginary numbers to express square roots of negative numbers

Find each sum or difference. Write answers in standard form. (2-5i) - (3+4i) - (-2+i)

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