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We had a question on an exam today that asked:

My Exam Paper wrote:What is the product of:
i . i ^ 2 . i ^ 3 . i ^ 4 ... i ^ 998 . i ^ 999

The '.' is multiplication, i is the imaginary number (root of -1, or j as it is known in such places as Python).

I came up with the answer 1, after assuming that I could use index laws and turn the indices into an arithmetic progression.

Is this right?

i . i ^2 . i^3 ... i^999
=
i ^(1+2+...+998+999)
=
i ^ 499500
(i^x has period four, 499500 modulo four equals 0)
=
i^0
=
1

so the answer looks correct to me

Combuster wrote:so the answer looks correct to me

'

Thanks - that was the hardest question on the exam, so it's good to know that I've been able to get it right