Hyperbolic function in real-imaginary form

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Hyperbolic function in real-imaginary form	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Hollie's copy of Hyperbolic function in real-imaginary form	draft	Hollie Tarr	16/02/2017 14:57

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Question statement

Express the function $f(z)=\simplify{{a1}*sinh({b1}*z)+{c1}*cosh({d1}*z)}$ in real-imaginary form $f(z)=g(x,y)+ih(x,y)$ , given that $z=x+iy$ .

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			Name	Type	Generated Value

a1	integer	0
c1	integer	1
b1	integer	3
d1	integer	5

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Generated value: `integer`

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1. Gap Gap 0. Mathematical expression
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2. Gap Gap 1. Mathematical expression
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$g(x,y)=$ Gap 0..

$h(x,y)=$ Gap 1..

Advice

Substitute $z=x+iy$ into the expression for $f(z)$ , so that

$f(z)=f(x+iy)=\simplify{{a1}*sinh({b1}*(x+iy))+{c1}*cosh({d1}*(x+iy))},$

then use the identity

$\simplify{{a1}*sinh(u+i*v)+{c1}*cosh(u+i*v)}=\simplify{{a1}*(sinh(u)*cos(v)+i*cosh(u)*sin(v))+{c1}*(cosh(u)*cos(v)+i*sinh(u)*sin(v))},$

and rearrange to give

$f(z)=\simplify{{a1}*sinh({b1}*x)*cos({b1}*y)+{a1}*i*cosh({b1}*x)*sin({b1}*y)+{c1}*cosh({d1}*x)*cos({d1}*y)+{c1}*i*sinh({d1}*x)*sin({d1}*y)}.$

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This question is used in the following exam:

Complex variables by Newcastle University Mathematics and Statistics in Content created by Newcastle University.

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Hyperbolic function in real-imaginary form

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`