No, it is not special, as long as you keep in mind that the complex numbers have the following form, called rectangular form:
z = x + iy, where x is called the real part of the number and y is called the imaginary part of the complex number.
Also, you should know that i is the square root of -1.
The 4 basic arithmetic operations are:
We'll treat "i" as a variable and we'll combine the real parts and imaginary parts together.
z1 = x1 + i*y1
z2 = x2 + i*y2
z1 + z2 = (x1 + x2) + i*(y1 + y2)
It is happening like in addition case, but we have to pay attention to the signs:
z1 - z2 = (x1 - x2) + i(y1 - y2)
We'll have to keep in mind that i^2 is turning into -1.
z1*z2 = (x1 + iy1)(x2 + iy2)
z1*z2 = x1*x2 + i*x1y2 + i*x2y1 + y1y2*i^2
z1*z2 = (x1x2 - y1y2) + i(x1y2 + x2y1)
Any division between 2 complex number has the following algorithm:
-firsat, we'll have to multiply the numerator by the conjugate of denominator, since we are not allowed to keep complex numbers to the denominator.
-then, we can separate the real part and the imaginary part.
z1/z2 = z1*z2'/z2*z2'