College Algebra Exercises Section 1.5
As you study these exercises, move your cursor over arrows, equal symbols, light bulbs, and highlighted words. Always check in with the wise old owl and his little apprentice by moving your cursor over them. Study with an active cursor.
| The definition that pops up when you move the cursor over a highlighted word is what should pop into your mind when you read, hear, or speak that word. | The material that pops up when you move the cursor over a light bulb is a suggested strategy for solving the problem. You should always formulate a similar strategy when you attempt to solve a problem. | When you move the cursor over an explanation of a step in a solution, the property that pops up is the mathematical justification for taking that action. You must always be able to provide such a justification for every step you take in mathematics. |
2.
Find real numbers a and b such that the
a + bi and 13 + 4i are .
Solution:
According to the definition of equality of complex numbers, these two complex numbers are equal if and only if their real
components are equal and their complex components are equal.
Therefore a = 13 and b = 4.
4. Find real numbers a and b such that the
(a + 6)+ 2bi and 6 - 5i are
.
Solution:
According to the definition of equality of complex numbers, these two complex numbers are equal if and only if there real
components are equal and their complex components are equal.
Therefore a + 6 = 6 and 2b = -5.
From which it follows that a = 0 and
6. Write the
in standard form.
Solution:
7. Write the
in standard form.
Solution:
8. Write the
in standard form.
Solution:
18. Compute the
(13 - 2i) + (-5 + 6i).
Solution:
(13 - 2i) + (-5 + 6i) = +
i = 8 +4i
20. Compute the
(3 + 2i) - (6 + 13i).
Solution:
21. Compute the
.
Solution:
25. Compute the
.
Solution:
27. Compute the product
.
Solution:
28. Compute the product
.
Solution:
32. Compute the
.
Solution:
Notice that 6 - 22i may be further simplified to 2(3 - 11i)
36. Compute the
.
Solution:
41. Write the
of 6 + 3i.
Solution:
The conjugate of 6 + 3i is 6 - 3i.
42. Write the
of 7 - 12i.
Solution:
The conjugate of 7 - 12i is 7 + 12i.
43. Write the
of
.
Solution:
The conjugate of
is
.
44. Write the
of
.
Solution:
The conjugate of
is
.
45. Write the
of
.
Solution:
The
of -20 is 
.
It then follows that
.
The conjugate of
is
.
Because
and
are equal, they have the same conjugates.
Therefore the conjugate of
is
.
46. Write the
of
.
Solution:
The
of -15 is 
.
The conjugate of
is
.
Because
and
are equal, they have the same conjugates.
Therefore the conjugate of
is
.
47. Write the
of
.
Solution:
The conjugate of
= 
is
= .
48. Write the
of
.
Solution:
The number is a real number and therefore is its own conjugate.
The conjugate of is .