Unit 10+ Complex Numbers Lesson 31 Operations with Complex Numbers 767

NAME: PERIOD: DATE:

Homework Problem Set

Express each of the following in a 1 bi form.

1. (2 1 5i) 1 (4 1 3i) 2. (21 1 2i) 2 (4 2 3i)

3. (4 1 i) 1 (2 2 i) 2 (1 2 i) 4. (5 1 3i)(5 2 3i)

5. (2 2 i)(2 1 i) 6. (1 1 i)(2 2 3i) 1 3i(1 2 i) 2 i

Express each of the following in a 1 bi form.

7. (1 1 i)2 8. (1 1 i)4 9. (1 1 i)6

2 t5 it4t3 1 21 4131

6810

4tit2 i Iti 25 151 91225 9Gt2531490

4TH2T IZ 23ft 32t3i4 Gl2ti 6122 ti 6CDZti 16

Kikki 4tD2Gti5 Cti 4CtiJI 2 Zi Zilt2iti2 412ttzittD 4Gt

768 Module 4 Quadratic Functions

10. Evaluate x2 2 6x when x 5 3 2 i.

11. Evaluate 4x2 2 12x when = −32 2

.x i

12. Show by substitution that −5 55i is a solution to 5x2 2 10x 1 6 5 0.

13. Use the fact that x4 1 64 5 (x2 2 4x 1 8)(x2 1 4x 1 8) to explain how you know that the graph of y 5 x4 1 64 has no x-intercepts. You need not find the solutions.

G D 6Gt3 i C3 i 6C3 i9 3i3142 18161I 611 181 619 1 18 100

4 5 12CEE4G CEE 18 614ftE Iatia 18619 3i 3iti2 18619 I 18

5Csf 2 100554 6 0 25 toirstsiD 1Ot2irst6SC Ifs 2 s irjt6 os 2ifsti2lotfirst65s irsffs.rs ioi airs 6 II EHf

The discriminant ofxZ4Xt8andX2t4xt8is 16

Neither equation canbefactored withoutusing complex S Therefore thesefunctions have no x intercepts