Tricky complex numbers problem

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Homework Help Overview

The problem involves complex numbers, specifically the rotation of one complex number, z2, around another complex number, z1, by an angle of 45 degrees.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the meaning of rotating a complex number around another point and explore the implications of the angle of rotation. There is a suggestion to use exponential notation for the rotation.

Discussion Status

Some participants are seeking clarification on the rotation concept, while others propose a method involving the difference between the two complex numbers and the application of a rotation formula. There is no explicit consensus on the interpretation of the problem.

Contextual Notes

Participants note that the original problem statement provided limited information, leading to various interpretations of the rotation process.

andrew.c
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Homework Statement



z1 = 1 + i, z2 = i − 5 are points in the complex plane. If z2 is rotated about z1 by 450
find its new position.

Attempt at solution
Absolutely no idea! I think I might need to use e^theta*i but not sure!
 
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What does that mean rotated about z1 by 450? Could you elaborate?
 
Sorry, that's all that was given...
I think it means like rotating 45 degs through the imaginary axis?
 
But then what does that have to do with Z1.
 
45 degrees is pi/4 radians. To rotate around another point, find the difference z2-z1 and rotate that by pi/4 (sure, multiply by e^(i*pi/4)). Add the result back to z1.
 
thank you!
 

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