Solution  Let z be =x  eˣ=-2 implies that  |-2|=2 and arg (-2)= 180°eˣ=2(cos180°+is in180°) eⁱˣ=cosx+isinx, eⁱˣ=cosx…

Solutions  Z=3z-10/(z-1)= z(z+1)=3z-10 Z²+z=3z-10 Z²+z-3z=-10 Z²-2z+10=0 Z=2±√(4-40)/(2)=2±6i/(2) Z₁=1+3i and z₂=1-3…

Solution   f(z)=(x-y)/(x²+y²)=x/(x²-y²)-it/(x²+y²) Therefore  U=x/(x²+y²), V=-y/(x²+y²) Equivalently  x=u/(u²-v²), y…

Solution . Let z= √(3-i) then r= √{(3)²+(-1)²}=√4=2 And arg tan⁻¹(-1/√3)=360°-30°=330°=11π/6 Therefore lnz ={lnr +(0º+…

Love gives a gig If f(z)= 2 with f(z)=1/z find the solution of the equation  f(z)=1/z=(x-iy)/x²+y²=x/(x²+y²) -iy/x²+y² …

Love gives a gig Find the fixed points of f(z) =(3z-10)/z+1     solution ⃗   multiply both sides by the denominator (z…

Love gives a gig Find the fixed points of f(z)=z² . solution         if z is a fixez point then  f(z)=z      z²=z     …