Question 1197056
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solve the equation z/z+1 = cos pi/4
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<pre>
Starting equation is

    {{{z/(z+1)}}} = {{{cos(pi/4)}}}.    (1)


Notice that {{{cos(pi/4)}}} = {{{sqrt(2)/2}}},  so your equation is

    {{{z/(z+1)}}} = {{{sqrt(2)/2}}}.


For brevity, I will use t for  {{{sqrt(2)/2}}}, so my equation is

    {{{z/(z+1)}}} = t.    (2)


From (2)

    z = t*(z+1)

    z = tz + t

    z - tz = t

    z(1-t) = t

    z = {{{t/(1-t)}}} = {{{((sqrt(2)/2))/(1-(sqrt(2)/2))}}} = {{{sqrt(2)/(2-sqrt(2))}}} = 2.414214  (rounded)


<U>CHECK</U>.  {{{2.414214/(2.414214+1)}}} = 0.707107 = {{{sqrt(2)/2)}}}.   ! correct !
</pre>

Solved.