A complex number *z* is of the form *x* + *iy*, where *x* and *y* are real numbers and *i* = √−1 is called the imaginary unit.

*x* is called the real part of *z* and is denoted as Re *z*.

*y* is called the imaginary part of *z* and is denoted as Im *z*.

Thus, *x* = Re *z*, *y* = Im *z*.

- Two complex numbers
*z*_{1}=*x*_{1}+*iy*_{1}and*z*_{2}=*x*_{2}+*iy*_{2}are equal, written as*z*_{1}=*z*_{2}, if and only if*x*_{1}=*x*_{2}and*y*_{1}=*y*_{2}.

**Note** Given two complex numbers *z*_{1} and *z*_{2}, we can only say *z*_{1} = *z*_{2} or *z*_{1} ≠ *z*_{2}. We cannot say *z*_{1} < *z*_{2} because there is no order relation in the field of complex numbers as in the field of real numbers.

The set of all complex numbers is denoted by *C*.

**Complex conjugate**If

*z*=*x*+*iy*is any complex number, then its conjugate**We can easily ...**

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