El conjunt dels nombres complexos [math]\mathbb{C}[/math] es defineix com el conjunt de combinacions lineals amb coeficients reals de la unitat real, 1, i la unitat imaginaria, i, que es definerix mitjançant la igualtat [math]i·i=-1[/math]. i.e., [br][br] [math]\mathbb{C}=\opencurlybrace z=a+b·i,[/math] conjuntoz is a point in the plane where the x-axis is measured in real units and the y-axis is measured[br]in imaginary units. Notice x=Re(z) and y=Im(z). [br][br]What is the locus of points that satisfy Re(z)=Im(z)?[br]What is the locus of points that satisfy Re(z)=3?[br]What is the locus of points that satisfy Im(z)=2?