Two questions in Complex analysis

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Can you please the highlighted questions numbers 17 and 19

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CHAP 118 Answers to selected odd-numbered problems begin on page ANS-10 EXERCISES 3.1 3.1.1 Limits z- て一之 lim z+1+i z + 7 2-2i z+1-i In Problems 1-8, use Theorem 3.1.1 and the properties of real limits on page 103 to compute the given complex limit. 2. 1. lim (z2 – z) Im (22) 4. lim 3. lim (12/2 – iz) z3i z + Re (z) z²+z² 6. lim 2-0 Re(z) + Im(z) 7. lim 8. lim (loge |x2 + y2] + i arctan 2-0 Im(z) 3) In Problems 9–16, use Theorem 3.1.2 and the basic limits (15) and (16) to compute the given complex limit. 9. lim (z? – z) 10. lim (z5 – z2 + z) 5. lim e? 2-i e² 2+1+i 2-12-1 2-> 11. lim (2+4) z► A/4 24 - 1 13. lim 2-izti z²+1 12. lim z►lti 22 – 1 z² – (2 + i) 14. lim 2+2+i Z – (2+i) z +3i2 16. lim z+-3+iv2 z2 + 6z + 11 (az +b) – (azo + b) 15. lim 220 z-zo Re(z) 17. Consider the limit lim z=0 Im(z) (a) What value does the limit approach as z approaches 0 along the line (b) What value does the limit approach as z approaches 0 along the imaginary axis? y = x? (c) Based on your answers for (a) and (b), what can you say about lim z–0 Im(z) 18. Consider the limit lim (z1 + i Arg (iz)). Re(z)? 2-> (a) What value does the limit approach as z approaches i along the unit circle [z] = 1 in the first quadrant? (b) What value does the limit approach as z approaches i along the unit circle |z| = 1 in the second quadrant? (c) Based on your answers for (a) and (b), what can you say about lim (z+ i Arg (iz))? 2→i 19. Consider the limit lim 2→0 (3) (a) What value does the limit approach as z approaches 0 along the real axis? (b) What value does the limit approach as z approaches 0 along the imaginary axis? (c) Do the answers from (a) and (b) imply that lim 2 (d) What value does the limit approach as z approaches 0 along the line y = x? () exists? Explain. 2-0 (e) What can you say about lim 2 NIIN ? zo
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I was having a hard time with this subject, and this was a great help.

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