- #1
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- TL;DR Summary
- Complex Variables by Stephen Fisher
Not hw, just reading the textbook. In section 1.5, page 50, the book goes through an explanation that [itex]\sin(x+iy)[/itex] is one-to-one if [itex]0 \le x < \pi/2[/itex] and [itex]y \ge 0[/itex]. At one point the book states that for [itex]1 = -e^{-i x_1}\,e^{-i x_2}\,e^{y_1}\,e^{y_2}[/itex] the absolute value of the left side is 1 and that of the right side is [itex]e^{y_1 + y_2}[/itex]. It then states that this result implies that [itex]-1 = e^{-ix_1-ix_2}[/itex].
I don't at all see why [itex]\left\vert-e^{-i x_1}\,e^{-i x_2}\,e^{y_1}\,e^{y_2}\right\vert = e^{y_1 + y_2}[/itex]. Can someone explain?
I don't at all see why [itex]\left\vert-e^{-i x_1}\,e^{-i x_2}\,e^{y_1}\,e^{y_2}\right\vert = e^{y_1 + y_2}[/itex]. Can someone explain?