A purely imaginary number is a complex number 
that has no real
part, i.e., ![Re[z]=0](/images/equations/PurelyImaginaryNumber/Inline2.svg)
.
The term is often used in preference to the simpler "imaginary" in situations
where 
can in general assume complex values with nonzero real parts, but in a particular
case of interest, the real part is identically
zero.
Purely Imaginary Number
See also
Complex Number, Complex Plane, Imaginary Number, Real PartExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Purely Imaginary Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PurelyImaginaryNumber.html