Question

What is the conjugate and the modulus of 6 − 3i?

Answer 1

bear in mind that the conjugate is the same pair with a different sign in between, so the conjugate of spaghetti - cheese is simply spaghetti + cheese and so on.  The modulus is simply $\sqrt{a^2+b^2}$

$\stackrel{a}{6}~~ \stackrel{b}{-3}i~~ \begin{cases} conjugate\\ \qquad 6+3i\\[-0.5em] \hrulefill\\ modulus\\ \qquad \sqrt{6^2+(-3)^2}\\ \qquad \sqrt{45}\\ \qquad 3\sqrt{5} \end{cases}$