For which real number k is (2 + ki)/(1 + 3i) a real number? What is its value then?
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
For which real number is a real number? What is its value then?
Need a reminder? The key ideaShow
. To divide, multiply the top and the bottom by the bottom with the sign of changed. The powers of repeat in fours: . So , where is the remainder of on division by .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The bottom. .
Step 2. The top. .
Step 3. Real means no imaginary part. , so .
Step 4. The value. .
Answer: , and the quotient is then .
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