5-4 Operations with Complex Numbers SWBAT

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Presentation transcript:

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

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

Evaluating Powers of i Simplify i63. Simplify i42.

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

Dividing Complex Numbers Simplify.

Simplify.

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

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.

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