Geometric description of set of points satisfying $\mathrm{Im}(z)>0$

Question

How can we describe geometrically the set of points $z$ satisfying the condition $\mathrm{Im}(z)>0$ where $z$ is a complex number?

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score 3 · Accepted Answer · 2013-04-08T00:00:38.223

3

If we write $z=x+yi$ with $x,y\in\mathbb R$ and draw this on the plane, we see that this is just the upper half plane, excluding the horizontal axis.

edited Apr 08 '13 at 00:00

answered Jan 01 '13 at 08:35

score 2 · Answer 2 · answered Jan 01 '13 at 08:34

2

Hint: If $z=x+yi$, $x,y\in \mathbb{R}$ and $\Im z>0$ then $y>0$ and $x\in \mathbb{R}$. What does this tell you?

answered Jan 01 '13 at 08:34

Nameless

2 Answers2