What is the value of cosh(1+i) ?

The value of cosh(1+i) is (cos(1)+e^2cos(1))/(2e)+i(-sin(1)+e^2sin(1))/(2e)

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cosh(1+i)

cosh (1 + i)

\frac{cos ( 1 ) + e ^{2} cos ( 1 )}{2 e} + i \frac{- sin ( 1 ) + e ^{2} sin ( 1 )}{2 e}

Solution steps

cosh (1 + i)

Use the Hyperbolic identity:

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

= \frac{e ^{1 + i} + e ^{- (1 + i)}}{2}

Simplify

\frac{e ^{1 + i} + e ^{- (1 + i)}}{2} : \frac{cos ( - 1 ) + e ^{2} cos ( 1 )}{2 e} + i \frac{sin ( - 1 ) + e ^{2} sin ( 1 )}{2 e}

= \frac{cos ( - 1 ) + e ^{2} cos ( 1 )}{2 e} + i \frac{sin ( - 1 ) + e ^{2} sin ( 1 )}{2 e}

Use the following property:

sin (- x) = - sin (x)

sin (- 1) = - sin (1)

= \frac{cos ( - 1 ) + e ^{2} cos ( 1 )}{2 e} + i \frac{- sin ( 1 ) + e ^{2} sin ( 1 )}{2 e}

Use the following property:

cos (- x) = cos (x)

cos (- 1) = cos (1)

= \frac{cos ( 1 ) + e ^{2} cos ( 1 )}{2 e} + i \frac{- sin ( 1 ) + e ^{2} sin ( 1 )}{2 e}

arcsin (sin (2 π))

sin (2.3)

sin (4 5^{\circ}) \cdot 3

sec (- \frac{π}{3}) - cot (- \frac{5 π}{4})

49 cos (3 0^{\circ})

What is the value of cosh(1+i) ?
The value of cosh(1+i) is (cos(1)+e^2cos(1))/(2e)+i(-sin(1)+e^2sin(1))/(2e)