Question

3 Evaluate( 2+i) squarerooted power 8​

Answer 1

Step-by-step explanation:

$( \sqrt{2 + i} ) {}^{8} = (2 + i) {}^{ \frac{1}{2} \times8 }$

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

Split this up

$(2 + i) {}^{2} \times (2 + i) {}^{2}$

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

Answer:

$(i+2)^4$

Step-by-step explanation:

assuming the equation is $(\sqrt{2+i})^8$ this simplifies to $(i+2)^4$ where i =$\sqrt{-1}$