段階的に解決し、人工知能を使用せず、優れた仕事を行いますご支援ありがとうございましたSOLVE STEP BY STEP IN DIGITAL FORMATDON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI |Obtain all the indicated roots of the number in question.1. 3/972.7-11i3. 10-5i4. -7-5i

Answered: Obtain all the indicated roots of the…

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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段階的に解決し、人工知能を使用せず、優れた仕事を行います
ご支援ありがとうございました
SOLVE STEP BY STEP IN DIGITAL FORMAT
DON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI |
Obtain all the indicated roots of the number in question.
1. 3/97
2.
7-11i
3. 10-5i
4. -7-5i

Expert Solution

Step 1: Some rule for argument

Given, x+iy is a complex number.

If (x,y) lies in 1st quadrant.

Then, principal argument = $tan to the power of negative 1 end exponent open parentheses y over x close parentheses$

If (x,y) lies in 2nd quadrant.

Then, principal argument = $straight pi minus tan to the power of negative 1 end exponent open parentheses open vertical bar straight y over straight x close vertical bar close parentheses$

If (x,y) lies in 3rd quadrant.

Then, principal argument = $tan to the power of negative 1 end exponent open parentheses open vertical bar y over x close vertical bar close parentheses minus straight pi$

If (x,y) lies in 4th quadrant.

Then, principal argument = $negative tan to the power of negative 1 end exponent open parentheses open vertical bar y over x close vertical bar close parentheses$