 # 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 𝒛𝟏 = 𝟏 + 𝟐𝒊:
The polar of a complex number is: 2 = 𝑟 ( 𝑐𝑜𝑠𝜃 + 𝑖 𝑠𝑖𝑛𝜃)
𝑎

Where 𝑟 = √𝑎2 + 𝑏 2 and 𝜃 = 𝑡𝑎𝑛−1 (𝑏) 𝑎 > 0
𝑎

= 𝑡𝑎𝑛−1 (𝑏) + 1000 𝑎 < 0, 𝑏 > 00𝑏 < 0
𝑎

=𝑡𝑎𝑛−1 (𝑏) + 3600 , 𝑎 > 0, 𝑏 > 0
r = √(1)2 + (2)2 = √5
2

𝜃 = 𝑡𝑎𝑛−1 (1) = 𝑡𝑎𝑛−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: √𝟓 𝐜𝐨𝐬(𝟏. 𝟏𝟎𝟕) , √𝟓 𝐬𝐢𝐧(𝟏. 𝟏𝟎𝟕)

For 𝒛𝟐 = −𝟑 + 𝟒𝒊
r = √(−3)2 + (4)2 = √5

4

θ = 𝑡𝑎𝑛−1 (−3) + 180
= −53.13 + 180
= 126.860 = 2.21 𝑟𝑎𝑑𝑖𝑎𝑛
= 5(cos(126.860 ) + 𝑖 sin(126. 860 ))
Hence, the polar coordinates would be: 𝟓(𝐜𝐨𝐬( 𝟏𝟐𝟔. 𝟖𝟔𝟎 ) + 𝟓 𝐬𝐢𝐧(𝟏𝟐𝟔. 𝟖𝟔𝟎 ))
For 𝒛𝟑 = −𝟓 − 𝟔𝒊
r = r = √(5)2 + (6)2 − √25 + 36 = 7.81
−6

θ = 𝑡𝑎𝑛−1 ( 5 ) + 180
= 50.19 + 180
= 230....

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