Discuss Discuss arithmetic of complex number. Is it special?
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'