Quiz on Analytic Functions

If f(z)=(x+ay)+i(bx+cy) is analytic then a,b,c equals to

• a=1,c=-b

• a=b=c=1

• a=-c,b=1

• a=-b,c=1

A point at which a function ceases to be analytic is called a

• Non-regular point

• Regular point

• Non-singular point

• Singular point

The function f(z)=|z| is a non-constant

• Analytic function

• nowhere analytic function

• entire function

• Non-analytic function

A function v is called a conjugate harmonic function for a harmonic function u in Ω whenever

• f(z)=u+iv is analytic

• v is analytic

• u is analytic

• f(z)=u-iv is analytic

A Milne - Thomson method is used to construct

• differentiable function

• continuous function

• harmonic function

• analytic function

A function ϕ(x,y) satisfying Laplace equation is called

• non-holomorphic function

• harmonic function

• analytic function

• holomorphic function

w=1z is known as

• inversion

• magnification

• translation

• rotation

W= z+α is known as

• inversion

• magnification

• translation

• rotation

If f(z) is analytic function and u is constant then

• f(z) is constant

• v is constant

• v is not constant

• both v and f(z) is constant

f(z)=ez is analytic

• only at z=0

• everywhere

• only at z=i

• nowhere