Question

3 Evaluate( 2+i) squarerooted power 8




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Answer 1

Explanation:

`( √(2 + i) ) {}^(8) = (2 + i) {}^{ (1)/(2) *8 }`

`(2 + i) {}^(4)`

Split this up

`(2 + i) {}^(2) * (2 + i) {}^(2)`

Use the Perfect Square Trinomial

`(a + b) {}^(2) = {a}^(2) + 2ab + {b}^(2)`

`(2 { }^(2) + 2(2)i + {i}^(2) )(2 {}^(2) + 2(2)i + {i}^(2)`

`{i}^(2) = - 1`

so

`(3 + 4i)(3 + 4i)`

`9 + 24i - 16`

`- 7 + 24i`

Answer 2

`(i+2)^4`

Explanation:

assuming the equation is
`(√(2+i))^8` this simplifies to
`(i+2)^4` where i =
`√(-1)`