Answer
conjugate: $12+5i$
modulus: 13
Work Step by Step
To find the conjugate of a complex number, reverse the sign of the imaginary part, as follows:
$\overline{12-5i}=12+5i$
Find the modulus using the formula $\sqrt{a^2+b^2}$ for $a+bi$, as follows:
$|12-5i|=\sqrt{12^{2}+(-5)^{2}}=\sqrt{144+25}=\sqrt{169}=13$
Hence,
conjugate: $12+5i$
modulus: $13$
