Question 1210634: Fill in the blanks to make a true statement.
___ + ____i * 2 = ___ + 60i + ___ + ___ i
Answer by KMST(5382)   (Show Source):
You can put this solution on YOUR website! This is sort of a riddle to make a student think of an answer, but there are many possible answers.
I was introduced to complex numbers in math as a 7th grader and much later reintroduced to them again as a college student.
This question could be from a young student, new to algebra, so I will try not to use many mathematical terms that such as student would not have heard before.
There are 3 complex numbers in that equation, represented as the "___ + ____i" before *2 , ___ + 60i, and the other ___ + ___ i.
All those blanks are to be filled with numbers that could all be different.
I would like to name the blanks  ,  ,  ,  , and  , in that order, to be able to tell those numbers apart.
If ___ + ____i is a complex number, then ___ + ____i*2 must mean the whole ___ + ____i complex number is multiplied times 2, not just its imaginary part.
Then, when filling the blanks with the letters above, I write
 .
I have to work with the real parts (a, c, and d) of those numbers separate from the imaginary parts d, 60, and e.
Then the problem becomes a set of equations that have to be made true at the same time, what we call a system of equations.
-->  -->  --> 
There are only 2 equations in the system to determine the 5 numbers a, b, c, d, and e.
Of course, 2 equations is not enough to determine a set of 5 numbers, so there will be many posible answers.
Any of the infinte number of solutions to that system of equations will make the statement true.
To make it simple I could choose  as part of the solution.
Then, substituting those values for a and b, I get  .
I still have many choices to finish finding a single set of values for my solution to that riddle.
For a simple solution, I could choose  as a solution to  .
After that, I just need to solve  -->  to have  as one solution to the problem,
and I could complete the blanks as
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