If i2 = -1 and if a is a positive integer, which of the following must be equal to ia ?A.ia+ 1B.ia+2C.ia+4D.i2a
Question
If i2 = -1 and if a is a positive integer, which of the following must be equal to ia ?A.ia+ 1B.ia+2C.ia+4D.i2a
Solution
The answer is D. i^2a
Here's why:
We know that i^2 = -1.
If a is a positive integer, then 2a is also a positive integer.
Therefore, i^2a = (i^2)^a = (-1)^a.
If a is an even number, (-1)^a = 1. If a is an odd number, (-1)^a = -1.
In either case, i^2a is a real number, not a complex number.
Therefore, the only possible answer is D. i^2a.
None of the other options (A, B, C) can be correct because they all result in a complex number (since they all include "ia" which is a complex number), not a real number.
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