loci-in-argand-diagrams

Loci in Argand diagrams

How do I sketch the locus of  or  on an Argand diagram?

• All complex numbers, , that satisfy the equation  lie on a vertical line with Cartesian equation 

  • Any complex number along this vertical line will have a real part of 

• All complex numbers, , that satisfy the equation <img alt=”Im blank z equals k” data-mathml='<math ><semantics><mrow><mi>Im</mi><mi> </mi><mi>z</mi><mo>=</mo><mi>k</mi></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″}</annotation></semantics></math>’ height=”22″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2222%22%20width%3D%2261%22%20wrs%3Abaseline%3D%2216%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%3EIm%3C%2Fmi%3E%3Cmi%3E%26%23xA0%3B%3C%2Fmi%3E%3Cmi%3Ez%3C%2Fmi%3E%3Cmo%3E%3D%3C%2Fmo%3E%3Cmi%3Ek%3C%2Fmi%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cs