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

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

Mathematics - Complex Number Question with Solution | TestHub

MathematicsComplex NumberPower of iotaEasy2 minPYQ_2023

MathematicsEasysingle choice

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

Answer:

Solution:

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

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

⏱ 2mℹ️ Source: PYQ_2023

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