Relations And Functions

Question

Find the value of the following :

$space space space space space space space space space space space space space space space open square brackets straight i to the power of 19 plus open parentheses 1 over straight i close parentheses to the power of 25 close square brackets squared$

Solution

space space space space space space space space space space space space space open square brackets straight i to the power of 19 plus open parentheses 1 over straight i close parentheses to the power of 25 close square brackets squared

space space space space space space space space space space space space open square brackets straight i to the power of 19 plus 1 over straight i to the power of 25 close square brackets squared equals open square brackets open parentheses straight i to the power of 19. straight i cubed close parentheses plus 1 over straight i to the power of 25. straight i cubed over straight i cubed close square brackets

space space space space space space space space space space space space space space space space space space space space space space space equals space open square brackets i cubed plus i cubed over i to the power of 28 close square brackets squared equals left square bracket i cubed plus i cubed right square bracket squared equals left square bracket 2 i cubed right square bracket squared

= 4i⁶ = 4i⁴ . i² = 4i² = 4(-1) = -4 (∵ i⁴ = 1

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