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A complete metric space is a metric space in which every Cauchy sequence is convergent. Examples include the real numbers with the usual metric, the complex numbers, ...

The extended complex plane is the name given to the complex plane with a point at infinity attached: C union {infty^~}, where infty^~ denotes complex infinity. It is also ...

The axis in the complex plane corresponding to zero real part, R[z]=0.

A pair of values x and y one or both of which is complex.

The portion of the complex plane z=x+iy with real part R[z]<0.

The unit lower half-disk is the portion of the complex plane satisfying {|z|<=1,I[z]<0}.

The portion of the complex plane {x+iy:x,y in (-infty,infty)} satisfying y=I[z]<0, i.e., {x+iy:x in (-infty,infty),y in (-infty,0)}

The negative real axis is the portion of the real axis with x<0.

The positive real axis is the portion of the real axis with x>0.

The portion of the complex plane z=x+iy with real part R[z]>0.