Question

hi guys

plz solve this questions with clear explanation .......
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Answer 1

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 2

Answer:

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