What can you say about z if |e|= 1. Ques
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
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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