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## Homework Statement

Suppose that w is a complex number which is not both real and [itex]\left\lfloor[/itex]w[itex]\right\rfloor[/itex][itex]\geq[/itex]1 (the absolute value of w).

Verify that Re[(1-w[itex]^{2}[/itex])[itex]^{1/2}[/itex]+iw]>0.

## Homework Equations

## The Attempt at a Solution

I attempted to solve this problem by dividing it into three cases; Im(w)>0, w[itex]\in[/itex](-1,1), and Im(w)<0. I could make the conclusion in the case of w[itex]\in[/itex](-1,1).

But, I don't have any idea how to approach in the cases of Im(w)>0 and Im(w)<0.

Could you give me a hint??