Goursat's theorem makes it easy to check differentiability of a function over this set. If a function over thisset is bounded and entire, then it is constant by Liouville's theorem. Fractional linear transformations namedfor Mobius take this set to itself. Extending this set by adjoining a point at infinity in this set allows for it to bemapped to 
Goursat's theorem makes it easy to check differentiability of a function over this set. If a function over thisset is bounded and entire, then it is constant by Liouville's theorem. Fractional linear transformations namedfor Mobius take this set to itself. Extending this set by adjoining a point at infinity in this set allows for it to bemapped to a sphere via stereographic projection. Differentiable functions from this set to itself satisfy theCauchy-Riemann equations and are referred to as holomorphic. This field is the algebraic closure of the realnumbers, and numbers of this type can be written in the form r times e to the i times theta. For 10 points,name this set of numbers which can be written in the form a + bi. 