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R Ravindra Pindel
Here is the solution:

G Gautam harsolia
Given problem is Now, we will reduce it into                                                                                                                                                                                                                                         Now, multiply numerator an denominator by                                            Therefore, answer is

G Gautam harsolia
Let  Now, multiply both numerator and denominator by  We will get,                                                                  We know that  Therefore, the least positive integral value of   is 4

G Gautam harsolia
It is given that Now, take  mod on both sides                                      Square both the sides. we will get Hence proved

G Gautam harsolia
Given problem is  Now, x = 0  is the only possible solution to the given problem Therefore, there are  0 number of  non-zero integral solutions of the equation

G Gautam harsolia
Let     and       It is given that and  Now,                                                                                                                                                                                                                                                                                                                                                      ...

G Gautam harsolia
it is given that   Now, expand the Left-hand side                                              On comparing real and imaginary part. we will get, Now,                                                 Hence proved

G Gautam harsolia
Let Now, we will reduce it into  Now, square and add both the sides. we will get, Therefore, modulus of     is   2

G Gautam harsolia
Let  Therefore, Now, it is given that  Compare (i) and (ii) we will get On comparing real and imaginary part. we will get On solving these we will get Therefore, the value of x and y are 3 and -3 respectively

G Gautam harsolia
Let Now, multiply the numerator and denominator by   Therefore, Square and add both the sides  Therefore, the modulus is    Now, Since the value of    is negative and the value of    is positive  and we know that it is the case in  II quadrant Therefore, Argument Therefore,  Argument and modulus are   respectively

G Gautam harsolia
It is given that  Therefore, NOw,                                             Now, Therefore, Therefore, the answer is 0

G Gautam harsolia
It is given that Now, And Now, Now, Therefore, the answer is

G Gautam harsolia
It is given that Now, we will reduce it into On comparing real and imaginary part. we will get Now,                                                    Hence proved

G Gautam harsolia
It is given that Then, Now, multiply the numerator and denominator  by    Now, Therefore, the value of      is

G Gautam harsolia
Given equation is   Now, we know that the roots of the quadratic equation are given by the formula In this case the value of    Therefore, Therefore, the solutions of requires equation are

G Gautam harsolia
Given equation is   Now, we know that the roots of the quadratic equation are given by the formula In this case the value of    Therefore, Therefore, the solutions of requires equation are

G Gautam harsolia
Given equation is   Now, we know that the roots of the quadratic equation are given by the formula In this case the value of    Therefore, Therefore, the solutions of requires equation are

G Gautam harsolia
Given equation is   Now, we know that the roots of the quadratic equation are given by the formula In this case the value of   Therefore, Therefore, the solutions of requires equation are