There are 7 questions in the attached file about polar coordinates and roots need to be solved

Anonymous
timer Asked: Feb 4th, 2019
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Question Description

please type the answers in steps.do your best please.

Tutor Answer

Super_Teach12
School: Cornell University

Here is the assignment :).. Allow me to me know if you have questions or need another help okay ;)

QUESTIONS:

Answer for Number 1:
Solution:
For π’›πŸ = 𝟏 + πŸπ’Š:
The polar of a complex number is: 2 = π‘Ÿ ( π‘π‘œπ‘ πœƒ + 𝑖 π‘ π‘–π‘›πœƒ)
π‘Ž

Where π‘Ÿ = βˆšπ‘Ž2 + 𝑏 2 and πœƒ = π‘‘π‘Žπ‘›βˆ’1 (𝑏) π‘Ž > 0
π‘Ž

= π‘‘π‘Žπ‘›βˆ’1 (𝑏) + 1000 π‘Ž < 0, 𝑏 > 00𝑏 < 0
π‘Ž

=π‘‘π‘Žπ‘›βˆ’1 (𝑏) + 3600 , π‘Ž > 0, 𝑏 > 0
r = √(1)2 + (2)2 = √5
2

πœƒ = π‘‘π‘Žπ‘›βˆ’1 (1) = π‘‘π‘Žπ‘›βˆ’1 2 = 1.107
r = 63.3%
Hence, the polar for of 𝑧1 = 1 + 2𝑖 would be √5(cos(1.107) + 𝑖 sin(1.107)
The polar coordinates would be: βˆšπŸ“ 𝐜𝐨𝐬(𝟏. πŸπŸŽπŸ•) , βˆšπŸ“ 𝐬𝐒𝐧(𝟏. πŸπŸŽπŸ•)

For π’›πŸ = βˆ’πŸ‘ + πŸ’π’Š
r = √(βˆ’3)2 + (4)2 = √5

4

ΞΈ = π‘‘π‘Žπ‘›βˆ’1 (βˆ’3) + 180
= βˆ’53.13 + 180
= 126.860 = 2.21 π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘›
= 5(cos(126.860 ) + 𝑖 sin(126. 860 ))
Hence, the polar coordinates would be: πŸ“(𝐜𝐨𝐬( πŸπŸπŸ”. πŸ–πŸ”πŸŽ ) + πŸ“ 𝐬𝐒𝐧(πŸπŸπŸ”. πŸ–πŸ”πŸŽ ))
For π’›πŸ‘ = βˆ’πŸ“ βˆ’ πŸ”π’Š
r = r = √(5)2 + (6)2 βˆ’ √25 + 36 = 7.81
βˆ’6

ΞΈ = π‘‘π‘Žπ‘›βˆ’1 ( 5 ) + 180
= 50.19 + 180
= 230....

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Anonymous
awesome work thanks

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