Question no 10 please! Question no 10 please! 10. (d) Number of complex numbers z satisfying z3 -i is = 2 , then the maximum value of Izl is equalt Share with your friends Share 0 Vijay Kumar Gupta answered this Dear Student, Let z=x+iy where x, y both are non zero real numbers.Then z3=z implies that x+iy3=x-iy .....1This further implies that, x3+iy3+3x2 iy+3xiy2=x-iy⇒ x3+i3y3+3x2 y i+3xi2y2=x-iy⇒ x3-y3i+3x2 y i-3xy2=x-iy⇒ x3-3xy2+i-y3+3x2 y=x-iyComparing real and imaginary parts on both sides, we get x3-3xy2=x and -y3+3x2 y=-y⇒ x2-3y2=1 and -3x2+y2 =1 Since x and y both are non zeroMultiplyin first equation with 3 and second equation with 1 and adding theresulting equations to get, 3x2-9y2+-3x2 +y2=3+1⇒-8y2=2⇒y2=-14The value of y comes out to be imaginary.So, we don not get any solutions from the above equation.However it can be noted that x,y=1,0 and x,y=0,1 satisfies the equation 1.At the point 1,0, we have LHS=1+i03=1 RHS=1-i0=1At the point 0,1, we have LHS=0+i13=i3=-i RHS=0-i1=-i Thus, we have two complex numbers satisfying the condition z3=z . Regards 2 View Full Answer