The complex number z = 3 + i is located 3 units to the right of the imaginary axis and 1 unit above the real axis, while w = ≡ + 2 i is located 1 unit left and 2 units up. For another, the sum of 3 + i and ≡ + 2 i is 2 + 3 i.Īddition can be represented graphically on the complex plane C. For instance, the sum of 5 + 3 i and 4 + 2 i is 9 + 5 i. To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts. The operations of addition and subtraction are easily understood. The numbers on the imaginary axis are sometimes called purely imaginary numbers. For instance, the real number 2 is 2 + 0 i.
X + yi when y is 0, that is, they're the numbers on the real axis. Real numbers are to be considered as special cases of complex numbers they're just the numbers When we use the xy-plane for the complex plane C, we'll call the x-axis by the name real axis, and the y-axis we'll call the imaginary axis. (Sometimes yi is called the imaginary part.) In general, the x part of a complex number z = x + yi is called the real part of z, while y is called the imaginary part of z. For example, the equation z = x + yi is to be understood as saying that the complex number z is the sum of the real number x and the real number y times i. We'll try to use x and y for real variables, and z and w for complex variables. The standard symbol for the set of all complex numbers is C, and we'll also refer to the complex plane as C. That gives us a second way to complex numbers, the first way being algebraically as in the expression x + yi. We'll even call it the complex plane when we use the xy-plane that way. Therefore, we can use the xy-plane to display complex numbers. Since Gauss proved the Fundamental Theorem of Algebra, we know that all complex numbers are of the form x + yi, where x and y are real numbers, real numbers being all those numbers which are positive, negative, or zero.
0 kommentar(er)
