help required in these q's (1 Viewer)

[amdspotter]

q1

q2

any help is appreciated

 

[amdspotter]

^^^

 

[icycledough]

Honestly for question 18, it's just brute manipulation and a lot of steps until you get the required answer. But if it helps, I would sub in z and then multiply the numerator and denominator by the conjugate of the denominator, so you can cancel out the 'i' terms and just be left with the real parts.

For question 1, I'm not sure if this would be the right way to go about it. But essentially, for z + w to be real, z and w have to be non-complex, conjugates of each other, or each of them will have a negative and positive complex part, so like z = 4 + i and w = 2 - i. For zw to be real, the only 2 conditions would be if z and w are both non-complex or if z and w are conjugates. As these 2 overlap with the previous condition, you can deduce that z has to be the conjugate of w or that z and w are non-complex (i.e their imaginary parts are 0).

 

[Drongoski]

Q18

 

[amdspotter]

Ah ok that makes sense thanks @icycledough and @Drongoski