For positive integers - n - 1 - n - 2 - the value of the expression- -1-i- - n1 - 1- -i - 3 - - n1 - 1- i - 5 - - n2 - -1- i - 7 - - n2 - where i-sqrt - -1 - is a real number and only if- n - 1 - n - 2 -1- n - 1 - n - 2 -1- n - 1 - n - 2 - n - 1 -0- n - 2 -0

Question

For positive integers - n - 1 - n - 2 - the value of the expression- -1-i- - n1 - 1- -i - 3 - - n1 - 1- i - 5 - - n2 - -1- i - 7 - - n2 - where i-sqrt - -1 -  is a real number and only if- n - 1 - n - 2 -1- n - 1 - n - 2 -1- n - 1 - n - 2 - n - 1 -0- n - 2 -0

Toppr Admin · Accepted Answer

For positive integers n1,n2 the value of the expression(1+i)n1+(1+i3)n1+(1+i5)n2+(1+i7)n2 where i=√−1 is a real number if and only ifn1=n2+1n1=n2−1n1=n2n1>0,n2>0

For positive integers $n_{1}, n_{2}$ the value of the expression ${(1 + i)}^{n 1} + ({1 {+ i}^{3})}^{n 1} + ({1 + i^{5})}^{n 2} + {(1 + i^{7})}^{n 2}$ where $i = \sqrt{- 1}$ is a real number if and only if
$n_{1} = n_{2} + 1$
$n_{1} = n_{2} - 1$
$n_{1} = n_{2}$
$n_{1} > 0, n_{2} > 0$