Conjugate of 1+i/1-i

1+i/1-i
(1+i)(1+i)/(1-i)(1+i)
1+2i-1/1+1
2i/2
i
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so the conjugate will be -i
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1+i                   i
___           =   

1-i


therefore the conjugate will be -i

P.S.-i have not shown the simplification . you can do it by rationalisation 
  • -1
Rationalise the denominator by multiplying and dividing by 1+i
You get:-

Z =(1+i/1-i)*(1+i/1+i) 
= (1+i)2/1-(-1)
=(1-1+2i)/2
= i
 
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-i
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Hope this helps u

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Z= 1+ i/ 1- i = 1+i/ 1- i * 1+ i / 1+ i ( bcoz to find conjugate we need to rationalize the term) = (1+ i)^2/(1^2 - i^2) = 1^2 + 2i + i^2/ 1+ 1 = 1-1+ 2i/ 2 = 2i/2 Therefore conjugate of Z = i
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