SOLUTION: Can you please help me by showing me how to solve the following. It says: Write the expression in the standard form a + bi. The problem is i^14. Thanks much!

All you have to know in all problem like this are these 5 facts: 

1.  i2 = -1
2.  (-1)even = 1
3.  (-1)odd = -1
4.  AB×C = (AB)C 
5.  AB+C = ABAC

i14 =  i2×7 = (i2)7 = (-1)7 = -1

Some other examples:

i682 = i2×341 = (i2)341 = (-1)341 = -1

i796 = i2×398 = (i2)398 = (-1)398 = 1

For odd powers of i, first write the exponent as an even number + 1:

i47 = i46+1 = i46i1 = i2×23i = (i2)23i = (-1)23i = -1i = -i

i109 = i108+1 = i108i1 = i2×54i = (i2)54i = (-1)54i = 1i = i

Edwin