Complex Expression Simplification
Hi
I have the expressions:
I1 := M*[1-a*exp(-i*theta)]/(1-b*cos(theta))
I2 := M*[1-a*i*exp(i*theta)]/(1+b*sin(theta))
I3 := M*[1+a*exp(-i*theta)]/(1+b*cos(theta))
I4 := M*[1+a*i*exp(i*theta)]/(1-b*sin(theta))
x1 := M*[1-a*cos(theta)]/(1-b*cos(theta))
x2 := M*[1+a*sin(theta)]/(1+b*sin(theta))
x3 := M*[1+a*cos(theta)]/(1+b*cos(theta))
x4 := M*[1-a*sin(theta)]/(1-b*sin(theta))
y1 := M*a*i*sin(theta)/(1-b*cos(theta))
y2 := M*a*i*cos(theta)/(1+b*sin(theta))
y3 := -M*a*i*sin(theta)/(1+b*cos(theta))
y4 := -M*a*i*cos(theta)/(1-b*sin(theta))
I enter the following expression
M1 := ((x1*y3-x3*y1)(I2-I4)-(x2*y4-x4*y2)(I1-I3))/((x1-x3)(y2-y4)+(x2-x4)(y3-y1))
and the initial expressions are automatically substituted (good). But how do I simplify the monster expression? Convert? Simplify? Factor? None seem to have positive outcomes. By hand I can reduce it quite well, but I want to be sure...
Also, can anyone recommend the optimal method of taking the expressions for I1, I2, I3, and I4, and solving for M in terms of these I's (canceling the a, b, and theta variables)?
Thanks!!!
Mike
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