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__Absolute value____:__

The **absolute value** (or *modulus* or *magnitude*) of a complex number *z* = r e^{iφ} is defined as |*z*| = *r*. Algebraically, if

*z* = *a* + *bi*, then

__Absolute Value Properties__

For all complex numbers z and w the following can be checked:

if and only if |
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__Distance:__

By defining the **distance function** d(z, w) = |z − w| we turn the set of complex numbers into a metric space and we can therefore talk about limits and continuity.

__ Conjugate__:

The **complex conjugate** of the complex number
*z* = *a* + *bi* is defined to be *
*. As seen in the figure,
is the "reflection" of z about the real axis.The following can be checked:

if and only if z is real | |
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if z is non-zero. |

To find out the