What is the value of sinh(2-3i) ?

The value of sinh(2-3i) is (-cos(3)+e^4cos(3))/(2e^2)+i(-sin(3)-e^4sin(3))/(2e^2)

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sinh(2-3i)

sinh (2 - 3 i)

\frac{- cos ( 3 ) + e ^{4} cos ( 3 )}{2 e ^{2}} + i \frac{- sin ( 3 ) - e ^{4} sin ( 3 )}{2 e ^{2}}

Solution steps

sinh (2 - 3 i)

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

= \frac{e ^{2 - 3 i} - e ^{- (2 - 3 i)}}{2}

Simplify

\frac{e ^{2 - 3 i} - e ^{- (2 - 3 i)}}{2} : \frac{- cos ( 3 ) + e ^{4} cos ( - 3 )}{2 e ^{2}} + i \frac{- sin ( 3 ) + e ^{4} sin ( - 3 )}{2 e ^{2}}

= \frac{- cos ( 3 ) + e ^{4} cos ( - 3 )}{2 e ^{2}} + i \frac{- sin ( 3 ) + e ^{4} sin ( - 3 )}{2 e ^{2}}

Use the following property:

sin (- x) = - sin (x)

sin (- 3) = - sin (3)

= \frac{- cos ( 3 ) + e ^{4} cos ( - 3 )}{2 e ^{2}} + i \frac{- sin ( 3 ) + e ^{4} ( - sin ( 3 ) )}{2 e ^{2}}

Use the following property:

cos (- x) = cos (x)

cos (- 3) = cos (3)

= \frac{- cos ( 3 ) + e ^{4} cos ( 3 )}{2 e ^{2}} + i \frac{- sin ( 3 ) + e ^{4} ( - sin ( 3 ) )}{2 e ^{2}}

Simplify

= \frac{- cos ( 3 ) + e ^{4} cos ( 3 )}{2 e ^{2}} + i \frac{- sin ( 3 ) - e ^{4} sin ( 3 )}{2 e ^{2}}

\frac{2.5}{tan ( 3 0 ^{\circ} )}

2 - 2 cos (2 π)

1 sin (4 0^{\circ})

sin^{2} (0.1)

22 sin (3 0^{\circ})

What is the value of sinh(2-3i) ?
The value of sinh(2-3i) is (-cos(3)+e^4cos(3))/(2e^2)+i(-sin(3)-e^4sin(3))/(2e^2)