Fishing
Challenge Setup and Instructions
Use your knowledge of complex operations to answer the following questions.
1. (7 + 2i4) + (-5 - i4)
Answer:
(7 + 2i4) + (-5 - i4)
= 7 - 5 + 2i4 - i4
= 2 + i4
= 2 + (i2)i2
= 2 + (-1)2
= 2 + 1 = 3
2. (-3-i) - (4+i)
Answer:
(-3-i) - (4+i)
= -3 - 4 - i - i
= -7 - 2i
3. (-2 + i2) x (-2 - i2)
Answer:
(-2 + i2) x (-2 - i2)
= 4 - 2i2 + 2i2 - i4
= 4- i4
= 4 - 1 = 3
4. (3 + i2) x (2 - i2)
Answer:
(3 + i2) x (2 - i2)
=6 - 3i2+2i2 - i4
= 6 - i2 - i4
= 6 - (-1) -1 = 6
5. (-7 - 2i) x (-3 - 2i)
Answer:
(-7-2i) x (-3 - 2i)
= 21 + 14i + 6i + 4i2
= 21 + 20i + 4(i2)
= 21 + 20i + 4(-1)
= 17 + 20i
6. (-4 + 2i4) x (-8 - 2i)
Answer:
(-4 + 2i4) x (-8 - 2i)
= 32 + 8i - 16i4 - 4i5
= 32 + 8i - 16(i2)2 -4i(i2)2
= 32 + 8i - 16(-1)2 - 4i(-1)2
= 32 + 8i - 16 - 4i
=16 + 4i
7. (-2 + i2) - (2 -i2)
Answer:
(-2 + i2) - (2 -i2)
= -2 -2 + i2 + i2
= -4 + 2(-1)
= -6
8. (-4 - 2i3 ) x (-6 + 2i3)
Answer:
(-4 - 2i3 ) x (-6 + 2i4)
= 24 - 8i4 + 12i3 - 4i7
= 24 - 8(i2)(i2) + 12(i2)i - 4(i2)(i2)(i2)i =
= 24 - 8(-1)(-1) + 12(-1)i - 4 (-1)(-1)(-1)i
=24 - 8 - 12i + 4i
= 16 - 8i
9. (7 - 3i4) x (-2 + 3i4)
Answer:
(7 - 3i4) x (-2 + 3i4)
= -14 + 21i
10. (2-3i4) + (7-2i3)
Answer:
(2-3i4) + (7-2i3)
= 9 - 3i4 - 2i3
= 9 -3(i2)2 -2(i2)i1
= 9 -3(-1)2 -2(-1)i1
= 9 -3 + 2i
= 6 + 2i
11. (4 + i2) + (4 - i2)
Answer:
= 8 + 4i2 - 4i2 + i2 - i2
= 8 + 0 + 0
= 8
12.
13. (-3 + 3i) - (-3 - 3i2)
Answer:
= -3 + 3 + 3i + 3i2
= 0 + 3i + 3i2
= 3i + 3(-1)
= -3 + 3i
14. (7 + 2i4) + (6 - 3i)
Answer:
= 13 + 2i4 - 3i
= 13 + 2(i)(i) - 3i
=13 + 2 (-1)(-1) - 3i
= 13 + 2 - 3i
= 15 - 3i
15. (3+i2) + (-2 + i2)
Answer:
= 3 + -2 + i2 + i2
= 1 + 2i2
= 1 + 2(-1)
= 1 + -2
= -1
16. (-3 + i) + (4 - i)
Answer:
(-3 + i) + (4 - i)
= -3 + 4 + i - i
= 1 + 0 = 1
17. (2 - i) x (2 - i)
Answer:
(-3 + i) + (4 - i)
= 4 - 2i - 2i + i
= 4 - 4i + 1
= 3 - 4i
18. (3+i2) + (-4 - i2)
Answer:
(3+i2) + (-4 - i2)
= 3 + -4 + i2 - i2
= -1 + 0 = -1
19. (3 + i2) x (2 - i2)
Answer:
(3 + i2) x (2 - i2)
= 6 - 3i2 + 2i2= i4
=6 - i2 - i4
= 6 - (-1) - 1 = 6
20. (-5 - i2 ) - (-2 - 3i4)
Answer:
(-5 - i2 ) - (-2 - 3i4)
= -5 + 2 - i2 + 3i4
= - 3 - (i2) + 3(i2)2
= - 3 - (-1) + 3(-1)2
= - 3 + 1 + 3
=1
