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What can you say about z if |e|= 1. Ques

What can you say about z if |e|= 1. Ques

Advanced Engineering Mathematics
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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(d) Arg()=Arg(2)-Arg(u) where Arg(2) denotes the principal argument of z. Question 2 What can you say about z if Je| = 1. Question 3 Find the roots of the following equations and hence plot the grid of complex plane which shows the roots. (a) 25 = -32i; (b) 24 = -8 – 8/3i; (c) 2 = -4+ 4i; (d) 23 = -9. Question 4 Factorize the following equations: (a) 22 – (1+ i)z + 6 – 17i; (b) 3:2 + (2— 3і): — 1- 3і, (c) 24+1. Question 5 Describe the points z in a complex plane that satisfy the following equations. Plot these points in a complex plane. (a) |2 – il = |2 – 1|; (b) Re(s) = |V3 – il; 1 (c) |z| = Re(2) + 2; (d) Re((1+i)z – 1) = 0; (e) [Im(iz) = 2; (f) 1 < |2 – 2i| < 4. Question 6 Solve the following equations: (a) 2:2 +z+ 3 = 0; (b) z? – (3 – 2i)z = 3i – 1.
Transcribed Image Text:(d) Arg()=Arg(2)-Arg(u) where Arg(2) denotes the principal argument of z. Question 2 What can you say about z if Je| = 1. Question 3 Find the roots of the following equations and hence plot the grid of complex plane which shows the roots. (a) 25 = -32i; (b) 24 = -8 – 8/3i; (c) 2 = -4+ 4i; (d) 23 = -9. Question 4 Factorize the following equations: (a) 22 – (1+ i)z + 6 – 17i; (b) 3:2 + (2— 3і): — 1- 3і, (c) 24+1. Question 5 Describe the points z in a complex plane that satisfy the following equations. Plot these points in a complex plane. (a) |2 – il = |2 – 1|; (b) Re(s) = |V3 – il; 1 (c) |z| = Re(2) + 2; (d) Re((1+i)z – 1) = 0; (e) [Im(iz) = 2; (f) 1 < |2 – 2i| < 4. Question 6 Solve the following equations: (a) 2:2 +z+ 3 = 0; (b) z? – (3 – 2i)z = 3i – 1.
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