1. Describe geometrically the sets of points z in the complex plane defined by the following relations: (a) 2-12-22] where 21, 22 € C. (b) 1/2=Z. (c) Re(z) = 3.
1. Describe geometrically the sets of points z in the complex plane defined by the following relations: (a) 2-12-22] where 21, 22 € C. (b) 1/2=Z. (c) Re(z) = 3.
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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![1. Describe geometrically the sets of points z in the complex plane defined by the
following relations:
(a) 221 222] where 21, 22 € C.
(b) 1/2 = 7.
(c) Re(z) = 3.
(d) Re(z) > c, (resp., 2 c) where e ER.
(e) Re(az + b) > 0 where a, b € C.
(f) |z| = Re(z) + 1.
(g) Im(z)e with CER.
2. Let (,) denote the usual inner product in R². In other words, if Z= (x₁, y₁)
and W = (2, 92), then
(Z, W) = x₁x2 +Y₁Y2.
Similarly, we may define a Hermitian inner product (,) in C by
(z, w) = zw.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F904caeb1-cd31-4dcf-9af8-09f5b2d51865%2F11c5de2a-7021-478f-afb5-655acbd119e4%2F5o59dnau_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Describe geometrically the sets of points z in the complex plane defined by the
following relations:
(a) 221 222] where 21, 22 € C.
(b) 1/2 = 7.
(c) Re(z) = 3.
(d) Re(z) > c, (resp., 2 c) where e ER.
(e) Re(az + b) > 0 where a, b € C.
(f) |z| = Re(z) + 1.
(g) Im(z)e with CER.
2. Let (,) denote the usual inner product in R². In other words, if Z= (x₁, y₁)
and W = (2, 92), then
(Z, W) = x₁x2 +Y₁Y2.
Similarly, we may define a Hermitian inner product (,) in C by
(z, w) = zw.
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