utkarshakash

Gold Member

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**1. Homework Statement**

Consider a line [itex]\alpha\overline{z}+\overline{\alpha}z+i\beta [/itex] such that [itex]\frac{-\alpha}{\overline{\alpha}} = \lambda(1+i), \lambda \in R^{+}[/itex], then the angle made by line with real axis is [itex]\dfrac{\pi}{k},[/itex] then k is

**2. Homework Equations**

**3. The Attempt at a Solution**

I have tried nearly every possible method but still did not get the answer. Suppose I substitute α in the equation of given line I get

[itex] (-\overline{\alpha}\lambda(1+i) )\overline{z}+\overline{\alpha}z+i\beta[/itex].

But I don't see any point in doing these things as it won't help me.

Second Method

The equation of line perpendicular to this line is given by

[itex]z\overline{\alpha}-\overline{z}\alpha+b[/itex] (for some 'b')

If somehow I could get the slope of this line I would get my answer. But the problem is how?