# Upper half-plane: Quiz

Question 1: It is the domain of many functions of interest in ________, especially elliptic modular forms.
Complex planeFunction (mathematics)Complex numberComplex analysis

Question 2: One natural generalization in differential geometry is hyperbolic n-space Hn, the maximally symmetric, simply connected, n-dimensional ________ with constant sectional curvature −1.
Differentiable manifoldRiemannian manifoldMetric tensorRiemannian geometry

Question 3: be the set of symmetric square matrices whose imaginary part is positive definite; that is the set of square matrices whose imaginary parts have positive ________.
Eigenvalue, eigenvector and eigenspaceLinear algebraVector spaceHilbert space

Question 4: In mathematics, the upper half-plane H is the set of ________ with positive imaginary part y.
Field (mathematics)Complex numberReal numberVector space

Question 5: The term is associated with a common visualization of complex numbers with points in the plane endowed with ________, with the Y-axis pointing upwards: the "upper half-plane" corresponds to the half-plane above the X-axis.
Cylindrical coordinate systemSpherical coordinate systemCartesian coordinate systemParabolic coordinates

Question 6: It also plays an important role in ________, where the Poincaré half-plane model provides a way of examining hyperbolic motions.
AlhazenBeltrami–Klein modelHyperbolic geometryNon-Euclidean geometry