i 57 + i 25 1 , when simplified has the value

i 57 + i 25 1 = ( i 4 ) 14 ⋅ i = i + i 1 ( ∵ i 4 = 1 ) + ( i 4 ) 6 ⋅ i 1 = i − i ( ∵ i 1 = − i ) = 0

Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberPower of iotaEasy2 minPYQ_2014

MathematicsEasysingle choice

$i^{57} + \frac{1}{i ^{25}},$ when simplified has the value

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Answer:

Solution:

$i^{57} + \frac{1}{i ^{25}} = (i^{4})^{14} \cdot i = i + \frac{1}{i} (∵ i^{4} = 1) + \frac{1}{( i ^{4} ) ^{6} \cdot i} = i - i (∵ \frac{1}{i} = - i) = 0$

Stream:BITSATSubject:MathematicsTopic:Complex NumberSubtopic:Power of iota

⏱ 2mℹ️ Source: PYQ_2014

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