imaginary part

More generally a complex number is called a period if its real and imaginary parts are periods.

It is an Eisenstein prime of the form with no imaginary part.

The real and imaginary parts of a complex number may be treated as separate dimensions.

These are easily seen to be the real and imaginary parts of the complex form .

The imaginary part of that function then defines the conjugate series.

The larger is the real part of the argument, the smaller should be the imaginary part.

The mode is specified separately, with the applied to both the real and the imaginary parts.

In order for a field to be charged, it must have two components that can rotate into each other, the real and imaginary parts.

The simplest cases, when the imaginary part of is zero, are:

For example, a programmer might create a new data type named "complex number" that would include real and imaginary parts.

The complex numbers are two-dimensional with a real part and an imaginary part.

To add two complex numbers, add the real and imaginary parts separately.

The three dimensional form in terms of the real and imaginary parts are:

(12.33) These are respectively the real and imaginary parts of (11.18).

To obtain the real conjugate, we discard the imaginary part of any coordinate.

In practice if (1) has real coefficients, the solutions based on y will have very small imaginary parts which must be discarded.

The imaginary part is plotted on the Y axis.

The real and imaginary parts of are plotted in the figure to the right with black and red curves.

Substituting the second equation into the first and using the fact that the imaginary part needs to be 0 results in:

The imaginary part of the inner product can be retrieved as follows:

The imaginary part is called the extinction coefficient.

Each such pair of root approach quickly and their imaginary part increases slowly logarithmic with n.

In general, the condition for linear instability is that the imaginary part of the "wave speed" c be positive.

Then any element of C can be decomposed into real and imaginary parts:

Let τ be a complex number with strictly positive imaginary part.