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
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. 