Practice Objectives
- Demonstrate the ability to add and subtract complex numbers
- Demonstrate the ability to multiply and divide complex numbers
Practice Adding, Subtracting, Multiplying & Dividing Complex Numbers
Instructions:
Answer 7/10 questions correctly to pass.
Simplify each, write your answer as:
$$a + bi$$
- a is the real part
- b is the imaginary part
- Fractions can be written using the "/" key
- Negative fractions can be written as -a/b or a/-b
- All fractions must be simplified
- Use 0 when needed:
- $$\text{Ex:} \, 3 = 3 + 0i$$
- $$\text{Ex:} \, 7i = 0 + 7i$$
Problem:
Correct! 
Not Correct! 
Your answer was: 0
The correct answer was: 0
Operations with Complex Numbers:
- To add two or more complex numbers, we add their real parts and add their imaginary parts
- Subtraction can be performed using addition of the opposite
- Alternatively, we can subtract their real parts and subtract their imaginary parts
- We multiply complex numbers using the commutative, associative, and distributive properties
- Replace any occurrence of i2 with -1
- Simplify by combining all real parts and all imaginary parts separately
- When we divide complex numbers, we need to eliminate i in the denominator
- For a denominator of the form a + bi, (a ≠ 0 and b ≠ 0):
- We multiply both numerator and denominator by the conjugate of the denominator
- The conjugate of a + bi is a - bi
- (a + bi)(a - bi) = a2 + b2
- For a denominator of the form bi, (b ≠ 0):
- We multiply both numerator and denominator by i if b < 0
- We multiply both numerator and denominator by -i if b > 0
- The denominator will become a positive real number
- For a denominator of the form a + bi, (a ≠ 0 and b ≠ 0):
Step-by-Step:
You Have Missed 4 Questions...
Invalid Character!
Simplified Form:$$a + bi$$
a =
b =
Current Score: 0%
Correct Answers: 0 of 7
Wrong Answers: 0 of 3
Need Help?
Video Lesson Written Lesson
Wow! You have mastered Operations with Complex Numbers!
Correct Answers: 0/0
Your Score: 0%
