
Subtraction We know that for any complex numbers z_{1} and z_{2}, there exists a complex number z such that z_{1} + z = z_{2}. This number z is denoted by z_{2}z_{1}. Let z_{1} = a+ib, z_{2} = c+id and z = x+iy, then z_{1} + z = z_{2} or (a+ib) + (x+iy) = c+id i.e (a+x) + i(b+y) = c+id a+x = c, b+y = d This system of equations has a unique solution x = ca, y = db Thus z = (ca) + i(db) Consequently, the difference z_{2}  z_{1} always exist with z = z_{2}  z_{1} = (c+id)  (a+ib) = (ca) + i(db) which yields the rule of subtraction of complex numbers.
Division of Complex Numbers
Example: Given the complex numbers z_{1>} = 3+i, z_{2} = 1+i, find the quotient z_{2}/z_{1} Directions: Solve the following questions. Also write at least 5 examples of your own for subtaction and division of complex numbers. 