If is a Complex no. . Then Find Min. value of

Results 1 to 2 of 2

- Jan 10th 2011, 09:06 PM #1

- Joined
- Dec 2010
- Posts
- 106
- Thanks
- 2

- Jan 11th 2011, 12:47 AM #2
Consider that . Now, surely, the value of z that minimizes this expression lies on the line between and and is, therefore, a real number.

In fact, it must be , for if you shift a that lies between and a little closer towards , without exceeding it, the first term of the sum gets larger but the second term gets smaller*by a larger amount*. This continues until you reach ; after that point on the real axis*both*terms increase.