A) \[\frac{4}{5}\]
B) \[0\]
C) \[\frac{2}{5}\]
D) \[-\frac{4}{5}\]
Correct Answer: D
Solution :
\[\frac{{{(1+i)}^{2}}}{i\,(2i-1)}=\frac{1+{{i}^{2}}+2i}{i\,(2i-1)}=\frac{2i}{i\,(2i-1)}\] \[=\frac{2(2i+1)}{4{{i}^{2}}-1}=\frac{4i+2}{-4-1}=-\frac{4}{5}i-\frac{2}{5}\] \[\therefore \] Imaginary part of\[\frac{{{(1+i)}^{2}}}{i(2i-1)}=-\frac{4}{5}\]
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