Question

Please helpp ive been stuck in this exercise for an hourrrr(mathh)

Answer 1

let's keep in mind that a conjugate is no more than the same "pair" but with a different sign between, so the conjugate of meow + quack is simply meow - quack, and so on, let's also recall that i² = -1.

`\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ -1-√(5)i\hspace{5em}\stackrel{conjugate}{-1+√(5)i} \\\\\\ (-1-√(5)i)(-1+√(5)i)\implies (-1)^2~~ - ~~(√(5)i)^2\implies (-1)^2~~ - ~~(√(5))^2 i^2 \\\\\\ 1~~ - ~~(√(5^2))i^2\implies 1~~ - ~~(5)(-1)\implies 1-(-5)\implies 1+5\implies \text{\LARGE 6}`