JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Analyzing +4 | -1

{z_1},\;{z_2},\; \ldots ,{z_n}

are complex numbers such that

\left| {{z_1}} \right| = \left| {{z_2}} \right| = ... = \left| {{z_n}} \right| = 1

, then

\left| {{z_1} + {z_2} + ... + {z_n}} \right|

is equal to

View answer and explanation

Correct option: C

\left| {\frac{1}{{{z_1}}} + \frac{1}{{{z_2}}} + ... + \frac{1}{{{z_n}}}} \right|

Option C is correct. Given the modulus of each complex number is 1, the expression

\left| {{z_1} + {z_2} + ... + {z_n}} \right|

is equal to

\left| {\frac{1}{{{z_1}}} + \frac{1}{{{z_2}}} + ... + \frac{1}{{{z_n}}}} \right|

because the conjugate of each

z_i

is its reciprocal.

More Questions from COMPLEX NUMBERS

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