 Hi and welcome to the session. I am Asha and I am going to help you with the following question which says find the number of non-zero integral solutions of the equation modulus 1 minus iota raised to the power x is equal to 2 raised to the power x. So, let us begin with the solution and we have to find the number of integral solutions of modulus 1 minus iota raised to the power x is equal to 2 raised to the power x and as we know if z is any complex number of the form a plus iota b then modulus of z is equal to root over a square plus p square therefore modulus of 1 minus iota will be root over 1 square plus minus 1 square raised to the power x is equal to 2 raised to the power x or root over 1 plus 1 raised to the power x is equal to 2 raised to the power x which further implies that root over 2 raised to the power x is equal to 2 raised to the power x is as possible only if we take x is equal to 0 thus number of non-zero integral solutions to the given equation is equal to 0 so answer is 0 which completes the solution hope you enjoyed it take care and have a good day.