Sure, if the imaginary part is opposite. For example:(3 + 2i) + (5 - 2i) = 8
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The set of real numbers are a subset of the set of complex numbers: imagine the complex plane with real numbers existing on the horizontal number line, and pure imaginary existing on the vertical axis. The entire plane (which includes both axes) is the set of complex numbers. So any real number (such as pi) will also be a complex number. But many people think of complex numbers as something that is "not a real number".
Rational and irrational numbers are real numbers. A complex number is represented by a+bi where a and b are real numbers. Zero is a real number therefore any real number is also complex whenever b=0
No. Negative four is a real number. All real numbers are also complex numbers, so it is a complex number (but it's real, not nonreal)
No. There are complex numbers and quaternions which are not real numbers.
It need not be. For example, a complex number as a percent of most other complex numbers, or any real number, will not be a real number.