Answer :
As we know that,
arg (z1z2) = arg(z1)+arg(z2) so,
arg (z1z2z3) = arg(z1)+arg(z2)+arg(z3)
arg((1+√3 i)(1+i)(cos θ+ i sin θ)
= arg(1+√3 i)+arg(1+i)+arg(cos θ + i sin θ).......... (1)
∴arg(z1 ) = θ
z2 = arg(1+i)
z3 = arg(cos θ + i sin θ)
⇒1(cos θ + i sin θ)
arg(z3 ) = θ
∵ In r(cos θ + i sin θ) , arg(z) = θ
By putting the value of all arg in 1, we get
Rate this question :
How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Expertsview all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
RELATED QUESTIONS :
Find the modulus
RS Aggarwal - MathematicsFind the modulus
RS Aggarwal - MathematicsFind the modulus
RS Aggarwal - MathematicsFind the modulus
RS Aggarwal - MathematicsFind the modulus
RS Aggarwal - MathematicsWrite 2i in polar
RS Aggarwal - MathematicsFind the principa
RS Aggarwal - Mathematics