Complex Number Assignment (1 Viewer)

deswa1

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Does anyone know how to solve this, I'm having great difficulty:

Solve for Z:

1/Z = 1 + i + 2/(1-i)

Any help would be appreciated, thanks :)
I'll just give a few pointers and if you still need more help, then I'll write more:

1. Put the RHS all on the same denominator
2. Take inverses of both sides
3. Realise the denominator
4. Finished
 

deswa1

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I got that Z = 1/2i I hope that's right :) Thank you so much, I was going towards substituting in Z = x + iy and everything, was getting messy :/
I didn't get that- I just did it very quickly so it might be wrong but I got z=(1-i)/4. Care to post your working?
 

alcronin

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1/Z = ((1+i)^2 + 2)/(1-i)
= (1+2i-1+2)/(1-i)
= (2i+2)/(1-i)
= (1+2i)/(1-i) X (1+i)/(1+i)
= (2+2i+2i-2)/(1+1)
= 4i/2
= 2i
therefore, Z = 1/2i


Sorry for it being hard to understand, they don't have equation editors on here :)
 

deswa1

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Why is your first line:

1/Z = ((1+i)^2 + 2)/(1-i) ?

It should be:

1/Z= ((1+i)(1-i) +2) /(1-i) because you are putting everything on top of 1-i
 

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