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The complex header implements complex numbers. Complex numbers are represented by the expression a + bi where a and b are real numbers and i is an imaginary unit that satisfies the constant expression i squared = -1.

Complex numbers allow imaginary solutions to expressions that have no actual solution. For instance, (x + 1) squared = -9 has no real solution, but does have two imaginary solutions when x = (a + bi), where a is -1 and b can be 3 or -3.

Note that library headers with an h extension are pre-standard headers. After standardisation, all library headers dropped the h extension including the complex header. Older compilers may still provide both versions of a library header, but in this day and age you should always use the standardised headers (no extension).

#include<complex.h> // non-standard

#include<complex> // standardised

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Q: What is the Main purpose of complex.h header file in c plus plus?
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