Hyperbolic Functions of a Complex Variable — Study Resources & PYQs
Hyperbolic functions defined for complex variables.
- Estimated study time: 30 minutes
Study resources
- Hyperbolic Functions (incl. complex variable) (Article) — Definitions of sinh, cosh, tanh, identities, derivatives/integrals and the link to trig functions via complex arguments.
- Complex Trigonometry / Logarithm (video) (Video) — Covers hyperbolic & inverse-hyperbolic functions of a complex variable and the logarithmic function of a complex variable within the full course.
- Logarithm of a Complex Variable (Article) — Logarithm of a Complex Variable — selected for the syllabus topic Hyperbolic Functions of a Complex Variable.
- MIT OpenCourseWare — Multivariable Calculus (Article) — MIT multivariable-calculus materials covering partial derivatives, homogeneous-function ideas, Taylor expansions, extrema and Lagrange multipliers.
Hyperbolic Functions of a Complex Variable previous year questions
- (a) Separate $\tanh(x + iy)$ into real and imaginary parts. (b) If $\tan(\alpha + i\beta) = x + iy$, then prove that (i) $x^2 + y^2 + 2x \cot 2\alpha = 1$, (ii…
- (a) If $\tan(\alpha + i\beta) = x + iy$, then prove that (i) $x^2 + y^2 + 2x \cot 2\alpha = 1$, (ii) $x^2 + y^2 - 2y \operatorname{coth} 2\beta = -1$. (b) Prov…
- (a) If $\tan(\alpha + i\beta) = x + iy$, then prove that (i) $x^2 + y^2 + 2x \cot 2\alpha = 1$, (ii) $x^2 + y^2 - 2y \coth 2\beta = -1$ (b) If $a + ib = c \tan…
- (a) If $\sin(\alpha + i\beta) = re^{i\theta}$, then show that $2r^2 = \cosh 2\beta - \cos 2\alpha$ and $\tan \theta = \tanh \beta \cot \alpha$. (b) If $\cosh x…
Taught in these subjects
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-1 — BMAT11 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu