Let $f = u + iv$ be analytic in a connected open set. If $u$ and $v$ satisfies $2u + 3v = 1$, then what will be the value of $f'(0)$ ? Since $f$ is analytic we know it satisfies Cauchy Riemann equation, also real and imaginary parts will be harmonic. But I couldn't get any conclusion about the function. Can someone provide an approach to solve this. Thanks in advance.
2026-03-10 14:48:41.1773154121
Derivative of function f at origin provided 2Ref + 3Imf = 1.
16 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in COMPLEX-ANALYSIS
- Minkowski functional of balanced domain with smooth boundary
- limit points at infinity
- conformal mapping and rational function
- orientation of circle in complex plane
- If $u+v = \frac{2 \sin 2x}{e^{2y}+e^{-2y}-2 \cos 2x}$ then find corresponding analytical function $f(z)=u+iv$
- Is there a trigonometric identity that implies the Riemann Hypothesis?
- order of zero of modular form from it's expansion at infinity
- How to get to $\frac{1}{2\pi i} \oint_C \frac{f'(z)}{f(z)} \, dz =n_0-n_p$ from Cauchy's residue theorem?
- If $g(z)$ is analytic function, and $g(z)=O(|z|)$ and g(z) is never zero then show that g(z) is constant.
- Radius of convergence of Taylor series of a function of real variable
Related Questions in DERIVATIVES
- Derivative of $ \sqrt x + sinx $
- Second directional derivative of a scaler in polar coordinate
- A problem on mathematical analysis.
- Why the derivative of $T(\gamma(s))$ is $T$ if this composition is not a linear transformation?
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Holding intermediate variables constant in partial derivative chain rule
- How would I simplify this fraction easily?
- Why is the derivative of a vector in polar form the cross product?
- Proving smoothness for a sequence of functions.
- Gradient and Hessian of quadratic form
Related Questions in COMPLEX-NUMBERS
- Value of an expression involving summation of a series of complex number
- Minimum value of a complex expression involving cube root of a unity
- orientation of circle in complex plane
- Locus corresponding to sum of two arguments in Argand diagram?
- Logarithmic function for complex numbers
- To find the Modulus of a complex number
- relation between arguments of two complex numbers
- Equality of two complex numbers with respect to argument
- Trouble computing $\int_0^\pi e^{ix} dx$
- Roots of a complex equation
Related Questions in ANALYTIC-FUNCTIONS
- Confusion about Mean Value Theorem stated in a textbook
- A question about real-analytic functions vanishing on an open set
- Prove $f$ is a polynomial if the $n$th derivative vanishes
- Show $\not\exists$ $f\in O(\mathbb{C})$ holomorphic such that $f(z)=\overline{z}$ when $|z|=1$.
- Riemann Mapping and Friends in a Vertical Strip
- How to prove that a complex function is not analytic in a rectangle?
- Prove or disprove that every Holomorphic function preserving unboundedness is a polynomial.
- If $f'$ has a zero of order $m$ at $z_0$ then there is $g$ s.t $f(z) - f(z_0) = g(z)^{k+1}$
- Schwarz lemma, inner circle onto inner circle
- Existence of meromorphic root for meromorphic function
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
If $2u+3v=1$, then $2u_x+3v_x=2u_y+3v_y=0$. Now, it is easy to deduce from the Cauchy-Riemann equations that $u$ and $v$ are constant functions. Therefore, $f$ is constant, and so $f'(0)=0$.