find the argument of 1 +√ 3 i
Share
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Answer:
Let z=
1+i
3
1−i
3
⇒z=
1+i
3
1−i
3
×
1−i
3
1−i
3
⇒z=
1+3
(1−i
3
)
2
⇒z=
4
1−3−2i
3
⇒z=−
2
1
−
2
i
3
r=
(−
2
1
)
2
+(−
2
3
)
2
=1
Comparing the above equation with z=rcosα+irsinα
rcosα=−
2
1
⇒cosα=−
2
1
rsinα=−
2
3
⇒sinα=−
2
3
Since sinα and cosα, both are negative, thus the argument will be in III
rd
quadrant.
α=180°+60°=240°(∵sin60°=
2
3
&cos60°=
2
1
)
Hence argument of given complex is 240°.