real part

The real part of a complex number is its “ordinary number” component — the piece with no i attached. In the number a + bi, the real part is a. If you imagine a complex number as a point on a map, the real part tells you how far east or west it sits; it is the horizontal coordinate.

The standard notation is Re(z). For z = a + bi we have Re(z) = a, and this a is always a genuine real number. A complex number is real exactly when its imaginary part is zero, in which case the number equals its own real part.

Watch one detail: the real part of 3 + 4i is 3, not 3 + 4i and not 4. It is just the single real number sitting in front of the imaginary piece, with the i stripped away.