hi guys
plz solve this questions with clear explanation .......
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:
12) It is given that z+1/z € R
this means,
z+1/z = z* +1/z*
z-z* = 1/z* - 1/z = z-z* / zz*
=> (z-z*)(zz*-1) = 0
However now, z-z* = 0 is not possible, as that would mean z is purely real, but that's not possible according to the given condition on Z that is an element of the set Complex numbers - Real numbers
So, zz* = 1
However, zz* = |z|^2 = 1
which means,
|z| = 1
13) |9z1z2 + 4z1z3 + z2z3| = 12
Dividing both sides by |z1z2z3|
=> | 9/z3 + 4/z2 + 1/z1 | = 12/(1)(2)(3) = 2
Now, 9/z3 = z3* since, |z3| = 3
Similarly, 4/z2 = z2*
and, 1/z3 = z3*
So,
|z1* + z2* + z3* | = 2
or
|(z1+z2+z3)*| = 2
So,
|z1+z2+z3| = 2
24) (1+√3i/1-√3i)^10
= ( e^iπ/3 / e^-iπ/3) ^10
= (e^i2π/3)^10 = e^i20π/3 = e^i(6π) * e^i(2π/3) = 1(-1/2+√3/2 i)
= -1/2 + √3/2i which is cis 2π/3
Answer:
PLEASE MARK FOR BRAINLIEST