Question

Evaluate:

Answer 1

We have the following expression,

[ i 18 + ( 1 i ) 25 ] 3

We know that, i= −1 .

Therefore, i 2 =−1 and i 4 =1 .

i 18 = i 4×4+2 = i 2 =−1

And

1 i = 1 i × i i = i i 2 =−i

Simplifying further

( 1 i ) 25 = ( −i ) 25 = ( −i ) 4×6+1 =−i

Hence,

[ i 18 + ( 1 i ) 25 ] 3 = [ −1−i ] 3 =−[ 1+ i 3 +3× 1 2 ×i+3×1× i 2 ] =−[ 1−i+3i−3 ] =2[ 1−i ]

Thus, [ i 18 + ( 1 i ) 25 ] 3 =2[ 1−i ] .