I'm studying complex analysis and I'm wondering about all complex values of $z$ that satisfy the equation: $$ \cosh(z)=0 \,\, . $$ Is there a smart way to show all values that vanish with the …

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points (cos t, sin t) form a circle …

Prove the following theorem: The zeros of $\sinh z$ and $\cosh z$ in the complex plane all lie on the imaginary axis. To be specific $$\sinh z=0$$ if and only if $z=n\pi i$ $(n=0,\pm1,2,...)...

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What is the general solution for cosh(z)=0 ? The general solution for cosh(z)=0 is No Solution for z\\in\\mathbb{R}

在 數學 中， 雙曲餘弦 是一種 雙曲函數，是 雙曲幾何 中，與歐幾里得幾何的 餘弦函數 相對應的函數。 雙曲餘弦一般以cosh表示 [1]，在部分較舊的文獻中有時會以 表示。 [2] 雙曲餘弦可以 …

在 數學 中， 雙曲餘弦 是一種 雙曲函數，是 雙曲幾何 中，與歐幾里得幾何的 餘弦函數 相對應的函數。 雙曲餘弦一般以cosh表示 [1]，在部分較舊的文獻中有時會以 表示。 [2] 雙曲餘弦可以 …

2015年9月7日 · The only solution to that is $2x = 0 \implies x = 0$. Alternatively, you can simply observe that $\cosh x$ is always non-zero, and the only solution comes from $\sinh x = 0$. …

2022年2月21日 · The hyperbolic cosine function is defined as: \[ \cosh z = \frac{e^z + e^{-z}}{2} \] Step 2: Set the equation \(\cosh z = 0\). This gives us: \[ \frac{e^z + e^{-z}}{2} = 0 \] Step 3: …

Show that (a) cos(iz) = cos(iz̅) for all z; (b) s̅i̅n̅(̅i̅z̅)̅ = sin(iz̅) if and only if z = nπi (n = 0, ±1, ±2, ...). engineering Using the definitions, prove: cosz is even, cos(-z)=cosz, and sinz is odd, sin(-z)= …