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  • Please help! - Complex numbers and quadratic equations - JEE Main-6

i^{41}+i^{90}+i^{100}+i^{123}  equals

  • Option 1)

    -2i

  • Option 2)

    -i

  • Option 3)

    0

  • Option 4)

    i

 

Answers (1)

ii^{41}+i^{90}+i^{100}+i^{123}=\left ( i^{4} \right )^{10}\cdot i+\left ( i^{4} \right )^{22}\cdot i^{2}+\left ( i^{4} \right )^{25}+\left ( i^{4} \right )^{30}\cdot i^{3}

=i+i^{2}+1+i^{3}

=i-1+1-i

=0

\therefore Option (C)


Option 1)

-2i

This is incorrect

Option 2)

-i

This is incorrect

Option 3)

0

This is correct

Option 4)

i

This is incorrect

Posted by

Vakul

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