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

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- Jan 10th 2011, 08:06 PMjacksMin. value
If is a Complex no. . Then Find Min. value of

- Jan 10th 2011, 11:47 PMFailure
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.