SOLUTION: solve the equation z/z+1 = cos pi/4

Question 1197056: solve the equation z/z+1 = cos pi/4
Answer by ikleyn(52804) (Show Source): You can put this solution on YOUR website!
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solve the equation z/z+1 = cos pi/4
~~~~~~~~~~~~~~~~~

Starting equation is

     = .    (1)


Notice that  = ,  so your equation is

     = .


For brevity, I will use t for  , so my equation is

     = t.    (2)


From (2)

    z = t*(z+1)

    z = tz + t

    z - tz = t

    z(1-t) = t

    z =  =  =  = 2.414214  (rounded)


CHECK.   = 0.707107 = .   ! correct !

Solved.

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