Please show your steps in details. Z is a complex number. 3. Let /(z= |Re z||Im...

Question

Question

Please show your steps in details.

Z is a complex number.
3. Let /(z= |Re z||Im zſ for all ze C. Show that $(z) is not differentiable at z=0.

Answer 1

Answer #1

f(z) - flay) = liretz) || Iml;)] Let z=xtiy. Retz) = * Im Cx) = g. f(x) = flang) = [tally! Eins 40-80)43-100 TERATE Czy)-(20)

Answer 2

Similar Homework Help Questions

ㆍ 3 (10) Let = Re', z = re (0<r< R) be two complex numbers. Show...

ㆍ 3 (10) Let = Re', z = re (0<r< R) be two complex numbers. Show the following identities hold: R2 2 OO = Re = 1 +2 C-z ΣΑ. R2 - 2rR cos (-0)r2 coS n(-e) n=1
Al. Practice with complex numbers: Every complex number z can be written in the form z...

Al. Practice with complex numbers: Every complex number z can be written in the form z r + iy where r and y are real; we call r the real part of z, written Re z, and likewise y is the imaginary part of z, y - Im z We further define the compler conjugate of z aszT-iy a) Prove the following relations that hold for any complex numbers z, 21 and 22: 2i Re (2122)(Re z) (Re z2) -...
Let f(z) = ee^z . Find Re(f), Im(f) and |f|

Let f(z) = ee^z . Find Re(f), Im(f) and |f|

complex analysis Let f(z) be continuous on S where for some real numbers 0< a <...

complex analysis Let f(z) be continuous on S where for some real numbers 0< a < b. Define max(Re(z)Im(z and suppose f(z) dz = 0 S, for all r E (a, b). Prove or disprove that f(z) is holomorphic on S.
3. Let f(z) = zc where c is a complex number. Assume that the domain of...

3. Let f(z) = zc where c is a complex number. Assume that the domain of f is the whole complex plane except the negative real numbers. a) What is the derivative of f? b) Let g(z) = cz. Find the derivative of g. 3. Let f(z) = zº where c is a complex number. Assume that the domain of f is the whole complex plane except the negative real numbers. a) What is the derivative of f? b) Let...
Please include step-by-step solution. (iv) Let a be any nonzero complex number. Show that for 12...

Please include step-by-step solution. (iv) Let a be any nonzero complex number. Show that for 12 – 20/ < |al, Z-Zo 2-20 n=0 n = 0 159)..ila). by a dr =0, 6, 11 d =0 Conclude that Z-ZO Z-ZO a for any closed (piecewise) regular curve y that lies in the disk (z – zo] < |al.

3. S how that if z is a complex number, a. Rele)-2 b. Im(2)- 2 2i...

3. S how that if z is a complex number, a. Rele)-2 b. Im(2)- 2 2i 2 ίθ d. sin θ 2i
10. Define the complex-valued function of a complex variable f:C- Cby 0, z-0 Show that the...

10. Define the complex-valued function of a complex variable f:C- Cby 0, z-0 Show that the Cauchy-Riemann equations hold at z 0 but that f is not differentiable at z 0.
Let z=6+6 \sqrt{3} i. (a) Graph z in the complex plane.

Let z=6+6 \sqrt{3} i.(a) Graph z in the complex plane. (b) Write z in polar form.(c) Find the complex number z9. (Enter your answer in a+bi form.) z9=

19. Which of the following statements are always true? (i) Re(2)Im(iz) 0 (ii) Re(iz)Im(z) = 0...

19. Which of the following statements are always true? (i) Re(2)Im(iz) 0 (ii) Re(iz)Im(z) = 0 (iii) z- Zi Im(z) = 0 (a) (ii) only (b) (i) only (c) (iii) only (d) (i) and (ii) only (e) (ii) and (ii) only