The complex function f: C→C is given by where is the conjugate of z. f(2)= (-112 + 17i) |z|², (a) If z = x+iy where a and y are real, express f(z) in the form u + iv, where u and are real. You must give your answers as real expressions in the variables x, y, using correct Maple syntax, for example, (2+3*x) * (4-y^5) +6*x*y/7. Answer: u= and v= . (b) Write down the equations that must be satisfied for f(z) to be differentiable at z + iy. Do not solve your equations at this stage, or simplify them in any way - you will do this in part (c). You must give your answer as a list of one or more equations in the variables and y, separated by commas and enclosed in square brackets, for example, [x=5*y, y=6-7*x^2]. As in this example, each equation must contain an equals sign=, not := . Answer: the following equations must be satisfied in order that f(z) be differentiable at z + iy (c) Find all points at which f(z) is differentiable, giving your answer as a list of one or more complex numbers, and enter your list in the box below. You must give exact answers in correct Maple notation, using a capital I for the complex number i. You may use fractions but not decimals, for example, [4, 5+6*1, (7/8)-9*1]. The order of the numbers in your list is not important. Submit Assignment Quit & Save Back Question Menu . Ne
The complex function f: C→C is given by where is the conjugate of z. f(2)= (-112 + 17i) |z|², (a) If z = x+iy where a and y are real, express f(z) in the form u + iv, where u and are real. You must give your answers as real expressions in the variables x, y, using correct Maple syntax, for example, (2+3*x) * (4-y^5) +6*x*y/7. Answer: u= and v= . (b) Write down the equations that must be satisfied for f(z) to be differentiable at z + iy. Do not solve your equations at this stage, or simplify them in any way - you will do this in part (c). You must give your answer as a list of one or more equations in the variables and y, separated by commas and enclosed in square brackets, for example, [x=5*y, y=6-7*x^2]. As in this example, each equation must contain an equals sign=, not := . Answer: the following equations must be satisfied in order that f(z) be differentiable at z + iy (c) Find all points at which f(z) is differentiable, giving your answer as a list of one or more complex numbers, and enter your list in the box below. You must give exact answers in correct Maple notation, using a capital I for the complex number i. You may use fractions but not decimals, for example, [4, 5+6*1, (7/8)-9*1]. The order of the numbers in your list is not important. Submit Assignment Quit & Save Back Question Menu . Ne
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The complex function f: C→C is given by
where is the conjugate of z.
f(z) = (-112+17i) |z|²,
(a) If z= x+iy where x and y are real, express f(z) in the form u + iv, where u and u are real. You must give your answers as
real expressions in the variables x, y, using correct Maple syntax, for example, (2+3*x) * (4-y^5) +6*x*y/7.
Answer: u=
and v=
BD.
(b) Write down the equations that must be satisfied for f(z) to be differentiable at x + ży. Do not solve your equations at this stage,
or simplify them in any way - you will do this in part (c). You must give your answer as a list of one or more equations in the variables
and y, separated by commas and enclosed in square brackets, for example, [x=5*y, y=6-7*x^2]. As in this example, each
equation must contain an equals sign =, not :=
Answer: the following equations must be satisfied in order that f(z) be differentiable at z + iy:
(c) Find all points at which f(z) is differentiable, giving your answer as a list of one or more complex numbers, and enter your list in
the box below. You must give exact answers in correct Maple notation, using a capital I for the complex number i. You may use
fractions but not decimals, for example, [4, 5+6*I, (7/8)-9*1]. The order of the numbers in your list is not important.
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Transcribed Image Text:The complex function f: C→C is given by
where is the conjugate of z.
f(z) = (-112+17i) |z|²,
(a) If z= x+iy where x and y are real, express f(z) in the form u + iv, where u and u are real. You must give your answers as
real expressions in the variables x, y, using correct Maple syntax, for example, (2+3*x) * (4-y^5) +6*x*y/7.
Answer: u=
and v=
BD.
(b) Write down the equations that must be satisfied for f(z) to be differentiable at x + ży. Do not solve your equations at this stage,
or simplify them in any way - you will do this in part (c). You must give your answer as a list of one or more equations in the variables
and y, separated by commas and enclosed in square brackets, for example, [x=5*y, y=6-7*x^2]. As in this example, each
equation must contain an equals sign =, not :=
Answer: the following equations must be satisfied in order that f(z) be differentiable at z + iy:
(c) Find all points at which f(z) is differentiable, giving your answer as a list of one or more complex numbers, and enter your list in
the box below. You must give exact answers in correct Maple notation, using a capital I for the complex number i. You may use
fractions but not decimals, for example, [4, 5+6*I, (7/8)-9*1]. The order of the numbers in your list is not important.
Quit & Save
Submit Assignment
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