What is the quotient of the complex number 4-3i divided by its conjugate?
1 answer:
Answer: C.
Step-by-step explanation:
1. You have the following division:
(As you can see, to find the conjugate of 4-3i you must change the sign between the terms).
2. To solve this division, you must multiply the numerator and the denominator by the conjugate of the denominator, as following:
3. Keeping on mind that , you have:
4. Simplifying:
5. The result is:
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Answer:
- 42
- 35
- 16
Step-by-step explanation:
Put the value where the variable is and do the arithmetic. It can save some steps to simplify the expression first.
35 -c³ +8 = 43 -c³
<u>c = 1</u>
43 - 1³ = 43 -1 = 42
<u>c = 2</u>
43 - 2³ = 43 -8 = 35
<u>c = 3</u>
43 -3³ = 43 -27 = 16
The values that go in the blanks are 42, 35, 16.
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<em>Additional comment</em>
It does not take long to learn how to use a spreadsheet for evaluating the same formula with a number of different values of the variable(s). Graphing calculators can do this, too. It is always appropriate to use the right tool for the job.
Familiarity with multiplication and addition facts is a very good place to start. It is also useful to memorize the squares and cubes of small integers. The latter are needed here.
