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

Created this.

Name	Status	Author	Last Modified
Function in real-imaginary form	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Hollie's copy of Function in real-imaginary form	draft	Hollie Tarr	16/02/2017 14:51

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Question statement

Express the function $f(z)=\simplify{{a1}*z^{n}-i*{b1}*z^{n-1}}$ 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	4
n2	integer	1
n3	integer	0
b1	integer	3
n	integer	2

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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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Gap-fill

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$g(x,y)=$ Gap 0..

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

Advice

All that is required in this question is to substitute $z=x+iy$ into the expression for $f(z)$ , and rearrange to the form $f(z)=g(x,y)+ih(x,y)$ , hence

$\begin{align}f(z)&=f(x+iy)\\&=\simplify{{a1}*(x+iy)^{n}-i*{b1}*(x+iy)^{n-1}}\\&=\simplify{{n2}*({a1}*(x^2-y^2)+{b1}*y) + {n3}*({a1}*(x^3-3*x*y^2)+{2*b1}*x*y)+i*({n2}*({2*a1}*x*y-{b1}*x)+{n3}*({3*a1}*x^2*y-{a1}*y^3-{b1}*(x^2+y^2)))}.\end{align}$

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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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Taxonomy: mathcentre

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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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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`