Solve the equation 7z/z+7 = 7+3i , z is an element of C

Answer 1

7z/(z+7) = 7 + 3i

7z/(z+7) - 7 = 3i

square both sides

49z^2/(z^2 + 14z +49) -98z/(z+7) + 49= -9

49z^2/(z^2+14z +49) - 98z/(z+7) =-58

multiply both sides by (z+7)^2

49z^2 - 98z^2 - 686z = -58z^2 -812z - 2842

9z^2 +126z -2842 = 0

use the quadratic formula

z = -126/18 + or - (1/18)sqr(126^2 +9(4)(2842))

simplify to get

z = -7 + (49/3)i

element of the set of complex numbers