Answer:
15. 5 -10i
16. 15+95i
17. 125
Step-by-step explanation:
15. The conjugate of a complex number is the same number but with an opposite imaginary part.
The real part of (5 +10i) is 5.
The imaginary part of (5+10i) is 10i. Its opposite is -10i.
So, the conjugate of (5 +10i) is (5 -10i).
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16. This question does not say what "the conjugate" is the conjugate of. In the above answers, we have assumed "the conjugate" to mean the answer to problem 15. (It might mean the conjugate of the numerator, since that is the subject of the question. We can't tell for sure.)
If we're to multiply the numerator (-7+5i) by the conjugate of the denominator (which conjugate is (5-10i)), we get ...
(-7 +5i)(5 -10i) = -7(5 -10i) +5i(5 -10i) = -35 +70i +25i -50i²
= -35 +50 +95i
= 15 +95i
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17. Again, we're not told the conjugate of what. It seems safe to assume that we're to multiply the denominator by its conjugate:
(5 +10i)(5 -10i) = 5(5 -10i) +10i(5 -10i) = 25 -50i +50i -100i²
= 125
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Additional comment
Taken together, these steps illustrate the process of finding the value of the ratio of two complex numbers:
(-7 +5i)/(5 +10i) = (15 +95i)/125 = 0.12 +0.76i
