help wit some questions (1 Viewer)

[prsce24]

1. Prove (1/z)=1/(|z)

|z = conjugate

2. z is a component of C such that z/z-i is real. Show that z is imaginary.

3. Solve the quadratic

ix^2 - 2(i+1)x + 10=0

Thank you

 

[CM_Tutor]

With question 1, do you mean prove that |1 / z| = 1 / |z|, or do you mean solve 1 / z = 1 / |z|, or something else?

With question 2, let z / (z - i) = k, where k is real (and k ≠ 1, as this would require z = i and hence make z / (z - i) undefined. Now, make z the subject, and you get z = ik / (k - 1), which is imaginary, provided k ≠ 1, as required.

With question 3, you need to use the quadratic formula. When you need to deal with √(-32i), you will need to show that if z² = -32i, then z = 4 - 4i or 4i - 4. I get the final answer as x = -1 - 3i or x = 3 + i

 

[prsce24]

With question 1, do you mean prove that |1 / z| = 1 / |z|, or do you mean solve 1 / z = 1 / |z|, or something else?

i mean to find the proof of (1/z)=1/(|z)
note ----- |z - say thats the sign for conjugate

 

[McLake]

i mean to find the proof of (1/z)=1/(|z)
note ----- |z - say thats the sign for conjugate

That is not true.

 

[CM_Tutor]

I agree with McLake.

 

[prsce24]

That is not true.

i agree too, but its in the cambridge book. : )

 

[withoutaface]

1/z= 1/(a+ib)=(a-ib)/(a²+b²)

1/(|z)=1/(a-ib)=(a+ib)/(a²+b²)

As can be seen. they are not equal.

Edit, I checked cambridge and there seems to be a _ above the 1/z that you have missed.

 

[McLake]

1/z= 1/(a+ib)=(a-ib)/(a²+b²)

1/(|z)=1/(a-ib)=(a+ib)/(a²+b²)

As can be seen. they are not equal.

Or more simlply:

Choose z = -i

1/i != 1/-i

 

[prsce24]

Edit, I checked cambridge and there seems to be a _ above the 1/z that you have missed.

hit me

thanx guys