36714

Question 1)
To have Z3 lie on the X axis, the imaginary numbers in Z1 and Z2 must cancel eachother out, with the real numbers being of equal value.

Eg. Z1= 2+i Z2= 2-i
Z3 is then 17 and on the x axis.

Question 2)
To work out where Z2 is, you must do the following
√(Z3-1)

Question 3)
(a+bi)(a-bi) will be a real number if a,b and c are real numbers and i is an imaginary numbers as they cancel each other out.

Questions 4)
To have Z3 lie on the y-axis, the real numbers must cancel each other out while the imaginary numbers CAN'T cancel out