# Question:Solve a set a of equation or a on complex equation

## Question:Solve a set a of equation or a on complex equation

Maple 2018

Dear experts

I am using Maple to solve a complex equation. My idea is to separate real and imaginary parts and then solve a set of the equation when both real and imaginary parts are zero. the following are the equation and the way I made real and imaginary parts;

eq:= (K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)+p*(-4*K^2*Q*(K^2+Q^2)+Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)-K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q)):

so the K and the Q are both complex variables and p and s are constant.

K:=Kr+I*Kim;

Q:= sqrt(K^2-I*h^2*2*Pi/1e-6);

therefore the real and imaginary parts of the equation are

finally, I tried to solve it as following

sys:={eval(A,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0,eval(B,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0}:

sol2:=fsolve(sys,{Kr=0..5,Kim=0..5},maxsols=5);

the problem is that Maple can not solve it and returns the command. I  know that there is solutions. How can I solve this equation?

the maple file is attached.mapleprime.mw

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I guess Maple use Newton method to solve equation or system of equations. Is there an alternative? I mean what are the possible methods?

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