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If the conjugate of a complex number is $\large\frac{1}{i-1},$ then the complex number is?

(A) $\large\frac{1}{i-1}$ (B) $\large\frac{-1}{i-1}$ (C) $\large\frac{1}{i+1}$ (D) $\large\frac{-1}{i+1}$
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Toolbox:
  • If $z=x+iy$ then $\overline z=x-iy$
$\overline z=\large\frac{1}{i-1}=\frac{1}{-1+i}$
$\therefore\:z=\large\frac{1}{-1-i}=\frac{-1}{i+1}$
answered Jul 3, 2013 by rvidyagovindarajan_1
 

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