For positive integers \[{{n}_{1}},{{n}_{2}}\]the value of the expression\[{{(1+i)}^{{{n}_{1}}}}+{{(1+{{i}^{3}})}^{{{n}_{1}}}}+{{(1+{{i}^{5}})}^{{{n}_{2}}}}+{{(1+{{i}^{7}})}^{{{n}_{2}}}}\]where \[i=\sqrt{-1}\]is a real number if and only if [IIT 1996]

For positive integers \[{{n}_{1}},{{n}_{2}}\]the value of the expressi

1.	For positive integers \[{{n}_{1}},{{n}_{2}}\]the value of the expression\[{{(1+i)}^{{{n}_{1}}}}+{{(1+{{i}^{3}})}^{{{n}_{1}}}}+{{(1+{{i}^{5}})}^{{{n}_{2}}}}+{{(1+{{i}^{7}})}^{{{n}_{2}}}}\]where \[i=\sqrt{-1}\]is a real number if and only if [IIT 1996]
A.	\[{{n}_{1}}={{n}_{2}}+1\]
B.	\[{{n}_{1}}={{n}_{2}}-1\]
C.	\[{{n}_{1}}={{n}_{2}}\]
D.	\[{{n}_{1}}>0,{{n}_{2}}>0\]
Answer» E.