1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

1.2 • THE ALCEBR.A OF COMPLEX NUMBERS 13

Definition 1.5: Real part

The real part of z, denoted Re (z), is the real number x. ~~~~~~~~

Definition 1.6: Imaginary part
The imaginary part of z, denoted Im (z), is the real number y.

Definition 1.7: Conjugate

The conjugate of z, denoted z, is the complex number (x, - y) = x -iy.

• EXAMPLE 1.4 a) Re (- 3 + 7i) = - 3 and Re((9, 4)] = 9. b) Im(-3 +

7i) = 7 and Im[(9, 4)] = 4. c) - 3 + 7i = - 3 - 7i and (9, 4) = (9, - 4).