Problem 1. Does there exist a complex number a such that a(1-2i, 3+5i) = (3-i, 2 + 6i)? Justify your answer.
Problem 1. Does there exist a complex number a such that a(1-2i, 3+5i) = (3-i, 2 + 6i)? Justify your answer.
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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![**Problem 1.** Does there exist a complex number \( \alpha \) such that
\[
\alpha (1 - 2i, 3 + 5i) = (3 - i, 2 + 6i)?
\]
Justify your answer.
---
In this problem, the question is whether there exists a complex number \( \alpha \) that can multiply a vector composed of complex numbers \((1 - 2i, 3 + 5i)\) to yield another vector \((3 - i, 2 + 6i)\).
This involves determining if \(\alpha\) can be a common factor for both components of the vectors after equalizing terms, typically resulting in solving two simultaneous complex equations, one for the real parts and one for the imaginary parts of the given vectors.
The solution involves analyzing whether a single complex number satisfies both transformed equations simultaneously.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac744b86-fb77-4dc8-9b17-1f74c21e67b7%2Fc9f2981e-c7bb-47db-a95c-db70fa846ab3%2Fdxln7tj_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 1.** Does there exist a complex number \( \alpha \) such that
\[
\alpha (1 - 2i, 3 + 5i) = (3 - i, 2 + 6i)?
\]
Justify your answer.
---
In this problem, the question is whether there exists a complex number \( \alpha \) that can multiply a vector composed of complex numbers \((1 - 2i, 3 + 5i)\) to yield another vector \((3 - i, 2 + 6i)\).
This involves determining if \(\alpha\) can be a common factor for both components of the vectors after equalizing terms, typically resulting in solving two simultaneous complex equations, one for the real parts and one for the imaginary parts of the given vectors.
The solution involves analyzing whether a single complex number satisfies both transformed equations simultaneously.
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