Express the following as a complex number in the form a + ib:

The complex conjugate of i4n-3, with n Î Z

By definition we know that i2 = -1

We know that i4n = i2·2·n = ((i2)2)n = ((-1)2)n = (1)n = 1

Since i4 = 1

i4n-3 = i4n-3i4 = i4n-3+4 = i4n+1 = i4ni1 = 1·i = i

Now we want the conjugate of i

The conjugate of A + Bi is A - Bi and vice-versa

We write i as 0 + i, so its conjugate is 0 - i, or -i, so

Answer = -i

Edwin
AnlytcPhil@aol.com