Answer
conjugate: $-1-2\sqrt{2}i$
modulus: $3$
Work Step by Step
To find the conjugate of a complex number, we reverse the sign of the imaginary part, as follows:
$\overline{-1+2\sqrt{2}i}$
$=-1-2\sqrt{2}i$
Find the modulus using the formula $\sqrt{a^2+b^2}$ for $a+bi$:
$|-1+2\sqrt{2}i|$
$=\sqrt{(-1)^{2}+(2\sqrt{2})^{2}}$
$=\sqrt{1+8}$
$=\sqrt{9}$
$=3$
Hence,
conjugate: $-1-2\sqrt{2}i$
modulus: $3$
