Question

The Greek letter iota, i, represents the square root of -1 (). We call i an imaginary unit. Any number that is a product of a real number and the imaginary unit i is called an imaginary number. Complex numbers are numbers that consist of a real part and an imaginary part. They are generally expressed as a + bi. In this task, you will find a pattern relating to the powers of i and also discover some identities involving complex numbers.

Use the identity i2 = -1 to compute the powers of i and complete the table.

Answer 1

Happy New Year from MrBillDoesMath!

Answer:

 i ^ (2n) = (i^2)^n = (-1)^n = -1 if n is odd and = 1 if n is even

 i ^ (2n+1) = i^(2n)* i =     -1 * i = -i if n is odd and =  1*i = i if n is even

Not sure if this answers your question but hopefully pushes you n the right direction.

Thank you,

MrB

Answer 2

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