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

idontknow Dec 2015 1,084 169 Earth Jan 26, 2020 #1 How many solutions does \(\displaystyle 3e^z -z=0 \) has in the disk \(\displaystyle |z|\leq 1\) ? z-complex .

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

topsquark Math Team May 2013 2,532 1,051 The Astral plane Jan 26, 2020 #3 idontknow said: How many solutions does \(\displaystyle 3e^z -z=0 \) has in the disk \(\displaystyle |z|\leq 1\) ? z-complex . Click to expand... 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 Reactions: idontknow

idontknow said: How many solutions does \(\displaystyle 3e^z -z=0 \) has in the disk \(\displaystyle |z|\leq 1\) ? z-complex . Click to expand... 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 Dec 2015 1,084 169 Earth Jan 27, 2020 #4 I took this from a pdf , now I lost the solution of the problem since I cannot find the pdf. Applying W-Lambert function may lead to a fast answer .

I took this from a pdf , now I lost the solution of the problem since I cannot find the pdf. Applying W-Lambert function may lead to a fast answer .

S SDK Sep 2016 804 545 USA Jan 27, 2020 #5 idontknow said: I took this from a pdf , now I lost the solution of the problem since I cannot find the pdf. Applying W-Lambert function may lead to a fast answer . Click to expand... The answer is 0 solutions. Use Rouche's theorem/argument principle. Reactions: topsquark and idontknow

idontknow said: I took this from a pdf , now I lost the solution of the problem since I cannot find the pdf. Applying W-Lambert function may lead to a fast answer . Click to expand... The answer is 0 solutions. Use Rouche's theorem/argument principle.