How To Find Sinh(x+iy) Formula - Proveiff Study

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Skip to content Posted inAbstract Algebra Advanced Math Complex Analysis Computer science Mathematics Mechanical Engineering Multivariable Calculus August 19, 2021Posted inAbstract Algebra, Advanced Math, Complex Analysis, Computer science, Mathematics, Mechanical Engineering, Multivariable Calculus

Question : Find sinh(x+iy) formula Solution : Let the complex number as \[z=sinh\left(x+iy\right)\] We know that \[\sin{\left(iz\right)}=isinh\left(z\right)\] So we shall multiply and divide by i we get \[z=\frac{isinh\left(x+iy\right)}{i}=\frac{\sin{\left(i\left(x+iy\right)\right)}}{i}=\frac{\sin{\left(ix-y\right)}}{i}\] Now we shall use formula of sin(A-B) =sin(A)cos(b) -cos(A) sin(B) \[z=\frac{\sin{\left(ix-y\right)}}{i}=\frac{\sin{\left(ix\right)}\cos{\left(y\right)}-\cos{\left(ix\right)}\sin{\left(y\right)}}{i}\] Now…

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