JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

For positive integers

{n_1},\;{n_2}

the value of the expression

{\left( {1 + i} \right)^{{n_1}}} + {\left( {1 + {i^3}} \right)^{{n_1}}} + {\left( {1 + {i^5}} \right)^{{n_2}}} + {\left( {1 + {i^7}} \right)^{{n_2}}},\;i = \sqrt { - 1} \;

is a real number if and only if

View answer and explanation

Correct option: D

{n_1} > 0,\;{n_2} > 0

Option D (n1 > 0, n2 > 0) is correct because the expression simplifies to a real number only if n1 and n2 are positive integers.

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