Question

the value of(i)^1/2+(-i)^1/2 is equal to​

Answer 1

Answer:

Required value of i^½ + ( - i )^½ is √( - 2i ).

Step-by-step explanation:

= > ( i )^( 1 / 2 ) + ( - i )^( 1 / 2 )

= > √{ ( i )^( 1 / 2 ) + ( - i )^( 1 / 2 ) }^2

Using,

( a + b )^2 = a^2 + b^2 + 2ab

= > √[ { i^½ }^2 + { - i^½ }^2 + 2( i^½ x - i½ ) ]

= > √[ ( i ) + ( - i ) + 2( - 1 x i^½ x i^½ ) ]

= > √[ i - i + 2( - 1 x ( i^½ )^2 ) ]

= > √{ 0 + 2( - 1 x i ) }

= > √( 2( - i )

= > $\sqrt{-2i}$

Hence the required value of i^½ + ( - i )^½ is √( - 2i ).