Question

Analytic Functions. Cauchy–Riemann Equations Check for analyticity by using (1) or (7). (Show the details of your work.) 1. f(z) = z^6 2. f(z) = i|z|^3 3. f(z) = e^x(cos y + i sin y) 4. f(z) = i/z^5 5. f(z) = z z? 6. f(z) = z + 1/z 7. f(z) = ln |z| + i Arg z 8. f(z) = 1/(1 - z^4) 9. f(z) = Re z/Im z 10. f(z) = Arg z 11. f(z) = Re (z^3) 12. f(z) = Re (z^2) - i Im (z^2)

          Analytic Functions. Cauchy–Riemann Equations
Check for analyticity by using (1) or (7). (Show the details of your work.)
1. f(z) = z^6
2. f(z) = i|z|^3
3. f(z) = e^x(cos y + i sin y)
4. f(z) = i/z^5
5. f(z) = z z?
6. f(z) = z + 1/z
7. f(z) = ln |z| + i Arg z
8. f(z) = 1/(1 - z^4)
9. f(z) = Re z/Im z
10. f(z) = Arg z
11. f(z) = Re (z^3)
12. f(z) = Re (z^2) - i Im (z^2)

Analytic Functions. Cauchy–Riemann Equations
Check for analyticity by using (1) or (7). (Show the details of your work.)
1. f(z) = z^6
2. f(z) = i|z|^3
3. f(z) = e^x(cos y + i sin y)
4. f(z) = i/z^5
5. f(z) = z z?
6. f(z) = z + 1/z
7. f(z) = ln |z| + i Arg z
8. f(z) = 1/(1 - z^4)
9. f(z) = Re z/Im z
10. f(z) = Arg z
11. f(z) = Re (z^3)
12. f(z) = Re (z^2) - i Im (z^2)

Added by David W.

Advanced Engineering Mathematics

Dennis G. Zill, Warren S. Wright 5th Edition

Chapter 17

Instant Answer

Solved by Expert Sri K

01/31/2023

Step 1

For the function f(z) = z3, we can see that the function is integrable over the interval from -1 to 1 because f(z) = z3 - 1 for all z within this interval. Show more…

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Analytic Functions. Cauchy-Riemann Equations Check for analyticity by using (1) or (7). (Show the details of your work.) 1. f(z) = z^6 2. f(z) = i|z|^3 3. f(z) = e^x(cos y + i sin y) 4. f(z) = i/z^5 5. f(z) = z z̄ 6. f(z) = z + 1/z 7. f(z) = ln |z| + i Arg z 8. f(z) = 1/(1 - z^4) 9. f(z) = Re z/Im z 10. f(z) = Arg z 11. f(z) = Re (z^3) 12. f(z) = Re (z^2) - i Im (z^2)