1. 5-4 Operations with Complex Numbers SWBAT
Perform operations with complex numbers.
Holt Algebra 2

2. The imaginary unit i can be raised to higher powers.
Notice the repeating pattern in each row of the table. The pattern allows you to express any power of i as one of four possible values: i, –1,
–i, or 1.
Helpful Hint

3. Evaluating Powers of i
Simplify –6i14.
–6i14 = –6(i2)7
= –6(–1)7
= –6(–1) = 6

4. Evaluating Powers of i
Simplify i63.
Simplify i42.

5. Conjugates: What is a conjugate? Factor x2 – 100.
Find the conjugate of the following:
1. (4 + i)
2. (i – 3)
3. (4i)
The complex conjugate of a complex number a + bi is a – bi.
Helpful Hint

6. Dividing Complex Numbers
Simplify.

7. Simplify.

8. The table shows several complex numbers, where i is the imaginary unit
The table shows several complex numbers, where i is the imaginary unit. Find the product of each set and put real, imaginary, or complex in the box depending on your answer.
8 – 2i 3 i
3 + 2i 5i -4
conjugate

9. Exit Card
Perform the indicated operation. Write the result in the form a + bi.
1. (2 + 4i) + (–6 – 4i)
2. (5 – i) – (8 – 2i)
3. (2 + 5i)(3 – 2i) 4.
5. Simplify i31.

10. Finish Worksheet Study for quiz tomorrow!
Homework
Finish Worksheet
Study for quiz tomorrow!