3.01 Complex Numbers

Jump Shot

1. (-8+i^[2])/(-3 + i^4)

Answer:

(-8+i^[2]/-3 + i^4)(-3-i^[4]/-3-i^[4])

= = (24 + 8i^[4] - 3i^[2] - i^[6]/9 - 3i^[4] + 3i^[4] - i^[8])

= (36/8) = (9/2)

2. (7+2i^[2])/(-3 + 2i)

Answer:

(7+2i^[2])/(-3 + 2i)(-3 - 2i/-3 - 2i)

= (-21 - 14i - 6i^[2] - 4i[3]/9 + 6i - 6i - 4i^[2])

= (-15- 10i/13) = (5[-3 - 2i]/13)

3. (3-2i^[2]/8-i)

Answer:

(3+2i^[2]/8 - i)(8 + i/8 + i)

= (24 + 3i - 16i^[2] - 2i^[3]/64 + 8i - 8i - i^[2])

(40 + 5i/65) = (8 + i/13)

4. (-5 + 2i^[4])/(4 + 3i^[2])

Answer:

(-5 + 2i^[4])/(4 + 3i^[2])(4-3i^[2]/4-3i^[2])

= (-20 + 15i^[2] + 8i^[4] - 6i^[4])/(16 - 12i^[2] + 12i^[2] - 9i^[4])

= -21/7 = -3

5. (-4 + 3i^[3])/(-5 - i^[2])

Answer:

(-4 + 3i^[3])/(-5 - i^[2])(-5+i^[2]/(-5 + i^[2])

= (20 - 4i^[2] - 5i^[3] + i^[5])/(25 - 5i^[2] + 5i^[2] - i^[4])

= (24 + 6i/24) = (4 + i/4)

6. (8 - i^[2]/4 + i^[4])

Answer:

(8 - i^[2]/4 + i^[4])(4 - i^[4]/4 - i^[4])

= (32 - 8i^[4] - 4i^[2] + i^[6]/16 - 4i^[4] + 4i^[4] - i^[8])

= 27/15

= 9/5

7. (7 + i^[4])/(-6 + 3i)

Answer:

= (-42 - 21i - 6i^[4] - 3i^[5]/36 + 18i - 18i - 9i^[2])

= (-48 - 24i/45)

= (-16 - 8i/15) =(8[-2 - i]/15)

8. (7 + i/5 + i^[3])

Answer:

(7 + i/5 + i^[3])(5 - i^[3]/5 - i^[3])

(35 - 7i^[3] + 5i - i^[4])/(25 - 5i^[3] + 5i^[3] - i^[6])

(34 + 12i/26) = (17 + 6i/13)

9. (-7 + 2i^[4])/(2 - i^[4])

Answer:

(-7 - 2i^[4]/2 - i^[4])/(2 + i^[4]/2 - i^[4])

= (-14 - -7i^[4] - 4i^[4] - 2i^[8]/4 + 2i^[4] - 2i^[4] - i^[8])

= (-27/3) = -9

10. (4 - 2i/7 + 3i^[4])

Answer:

(4 - 2i/7 + 3i^[4])(7 - 3i^[4]/7 - 3i^[4])