Question

`[i^18 + (1/i)^25]^3` का मान ज्ञात कीजिए।

Answer 1

`[i^18 + (1/i)^25]^3 = [(i^2)^9 +  1 /((i^2)^12 i)]^3`

= ` [(-1)^9 +  1 /((-1)^12 i)]^3`

= `[ -1  + 1/i  xx  i/i]^3`

= `[- 1 -i]^3 = - (1 + i)^3`

अब `[ (a + b)^3 = [a^3 + 3a^2b + 3ab^2 + b^3]`

= - (1 + 3i + 3i² + i²)

= - (1 + 3i - 3 + i² .i )

= (- 2 + 3i – i)

= – (- 2 + 2i)

= 2 – 2i