# Complex Numbers - Video Tutorials & Practice Problems

## Introduction to Complex Numbers

Identify the real and imaginary parts of each complex number. $-4-9i$

$a = -9, b = -4$

$a = -4, b = -9$

$a = 4, b = 9$

$a = -4, b = 9$

Identify the real and imaginary parts of each complex number. $3+2i\sqrt3$

$a=3,b=2\sqrt3$

$a = 3, b = 2$

$a=2\sqrt3,b=3$

$a=3,b=\sqrt3$

Write the complex number in standard form. $\frac{9+\sqrt{-16}}{3}$

$3+4i$

$9+16i$

$3+\frac43i$

$\frac{13i}{3}$

## Adding and Subtracting Complex Numbers

Find the difference. Express your answer in standard form. $\left(2+8i\right)-\left(4-i\right)$

$-2+9i$

$6+7i$

$2+7i$

$2-9i$

Find the sum. Express your answer in standard form. $5\left(4+7i\right)+6\left(3-2i\right)$

$7+5i$

$38+23i$

$2+47i$

$7+9i$

## Multiplying Complex Numbers

Perform the indicated operation. Express your answer in standard form. $\left(3+8i\right)^2$

$-55+48i$

$9+64i$

$24i$

$9+24i$

Find the product. Express your answer in standard form. $2i\left(9-4i\right)\left(6+5i\right)$

$8+18i$

$54-20i$

$54-40i$

$-42+148i$

## Complex Conjugates

Find the product of the given complex number and its conjugate. $4-5i$

$16$

$41$

$25$

$20$

Find the product of the given complex number and its conjugate. $-7-i$

$50$

$14$

$49$

$1$

## Dividing Complex Numbers

Find the quotient. Express your answer in standard form.

$\frac{6+i}{4-2i}$

$\frac{11}{10}+\frac45i$

$\frac65+\frac45i$

$\frac{11}{10}-\frac45i$

$22+16i$

Find the quotient. Express your answer in standard form.

$\frac{-5+3i}{-7-4i}$

$\frac35+\frac45i$

$18i$

$23-41i$

$\frac{23}{65}-\frac{41}{65}i$

## Do you want more practice?

- In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 - 4i)
- In Exercises 1–8, add or subtract as indicated and write the result in standard form. (3 + 2i) - (5 - 7i)
- In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 - (- 5 + 4i) - (- 13 ...
- Decide whether each statement is true or false. If false, correct the right side of the equation. √-25 = 5i
- Decide whether each statement is true or false. If false, correct the right side of the equation. i^12 = 1
- Decide whether each statement is true or false. If false, correct the right side of the equation. (-2+7i) - (1...
- In Exercises 9–20, find each product and write the result in standard form. (7 - 5i)(- 2 - 3i)
- In Exercises 9–20, find each product and write the result in standard form. (3 + 5i)(3 - 5i)
- In Exercises 9–20, find each product and write the result in standard form. (- 5 + i)(- 5 - i)
- Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptio...
- Identify each number as real, complex, pure imaginary, or nonreal com-plex. (More than one of these descriptio...
- Write each number as the product of a real number and i. √-25
- Perform each operation. Write answers in standard form. 15i- (3+2i) -11
- In Exercises 21–28, divide and express the result in standard form. 2i/(1 + i)
- Perform each operation. Write answers in standard form. (-8+2i)(-1+i)
- In Exercises 21–28, divide and express the result in standard form. 5i/(2 - i)
- Perform each operation. Write answers in standard form. (5-11i)(5+11i)
- In Exercises 21–28, divide and express the result in standard form. 8i/(4 - 3i)
- Find each product or quotient. Simplify the answers. √-13 * √-13
- Find each product or quotient. Simplify the answers. √-3 * √-8
- In Exercises 29–36, simplify and write the result in standard form. √-108
- Find each product or quotient. Simplify the answers. √-30 / √-10
- In Exercises 29–36, simplify and write the result in standard form. √(3^2 - 4 × 2 × 5)
- Simplify each power of i. i^1001
- In Exercises 29–36, simplify and write the result in standard form. √(1^2 - 4 × 0.5 × 5)
- Simplify each power of i. i^-27
- Simplify each power of i. 1/i^17
- Write each number in standard form a+bi. -6-√-24 / 2
- Write each number in standard form a+bi. 10+ √-200 / 5
- In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)^2
- Write each number in standard form a+bi. -3+ √-18 / 24
- 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. (- 6 - √-12)/48
- Find each sum or difference. Write answers in standard form. (2-5i) - (3+4i) - (-2+i)
- Find each sum or difference. Write answers in standard form. (-4-i) - (2+3i) + (-4+5i)
- Find each sum or difference. Write answers in standard form. 3√7 - (4√7-i) -4i + (-2√7+5i)
- In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^44
- In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^114
- In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^135
- Find each product. Write answers in standard form. (3+i)(3-i)
- Find each product. Write answers in standard form. (-2-3i)(-2+3i)
- Find each product. Write answers in standard form. (√6+i)(√6-i)
- In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (2 - 3i)(1 - i)...
- In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (8 + 9i)(2 - i)...
- In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (2 + i)^2 - (3 ...
- Find each product. Write answers in standard form. (3-i)(3+1)(2-6i)
- Evaluate (x^2 + 19)/(2 - x) for x = 3i.
- Find each quotient. Write answers in standard form. 2-i / 2+i
- Find each quotient. Write answers in standard form. 1-3i / 1+i
- Simplify each power of i. i^25
- Simplify each power of i. i^29
- Simplify each power of i. i^26
- In Exercises 95–99, perform the indicated operations and write the result in standard form. 4/(2 + i)(3 - i)
- In Exercises 95–99, perform the indicated operations and write the result in standard form. (1 + i)/(1 + 2i) ...
- Simplify each power of i. i^-14
- Simplify each power of i. 1/i^-11
- Simplify each power of i. 1/i^-12