2. Equations and Inequalities

Simplify square roots of negative numbers.

Complex Numbers

Imaginary roots of negative numbers | Imaginary and 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)

Pre-Calculus - Simplify powers of i

Subtract complex numbers: combining like terms

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)

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

i^135

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

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

Complex Numbers: Dividing - Ex 2

Simplify positive integer powers of i

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

(- 3 - √-7)^2

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)

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

Add complex numbers by combining like terms

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

i^44

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

Perform Operations with Square Roots of Negative Numbers

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

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

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

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

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

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

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)

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 

Multiplying square roots of negative numbers

Complex Numbers: Dividing - Ex 1

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)

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

Rewriting Powers of  ' i  '  - Ex 2

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

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)

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)

Rationalize Denominator with Imaginary Part in Complex Number

Subtract complex numbers

Evaluate higher powers of i

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

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