# How many solutions ?

#### idontknow

How many solutions does $$\displaystyle 3e^z -z=0$$ has in the disk $$\displaystyle |z|\leq 1$$ ? z-complex .

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#### topsquark

Math Team
How many solutions does $$\displaystyle 3e^z -z=0$$ has in the disk $$\displaystyle |z|\leq 1$$ ? z-complex .
Let z = x + iy.

Then
$$\displaystyle 3 e^{x + iy} - (x + iy) = 0$$

Use Euler's exponential equation to get rid of the exponential, then separate the equation into real and complex parts. Solve the equations. (The x equation is annoying but can be done numerically using W|A or something.

-Dan

idontknow

#### idontknow

I took this from a pdf , now I lost the solution of the problem since I cannot find the pdf.