No Complex number is the sum of a real and a imaginary part. Every complex number is not real number. But every real number can be said as complex number considering imaginary part zero. A is real part & B is imaginary part.
Similarly, you may ask, what is the imaginary part of a complex number?
The real part of a complex number z is denoted by Re(z) or ℜ(z); the imaginary part of a complex number z is denoted by Im(z) or ℑ(z). For example, A real number a can be regarded as a complex number a + 0i whose imaginary part is 0. A purely imaginary number bi is a complex number 0 + bi whose real part is zero.
What is a complex number system?
A complex number is a number of the form a + bi, where a and b are real numbers and i is an indeterminate satisfying i2 = −1. For example, 2 + 3i is a complex number. The real number a is called the real part of the complex number a + bi; the real number b is called the imaginary part of a + bi.
What is the real part of?
A nonzero complex number with zero real part is called an imaginary number or sometimes, for emphasis, a purely imaginary number.