Appendix G - Complex Numbers - G Exercises - Page A55: 15

conjugate: $12+5i$ modulus: 13

To find the conjugate of a complex number, we reverse the sign of the imaginary part, like so: $\overline{12-5i}=12+5i$ We find the modulus using the formula $\sqrt{a^2+b^2}$ for $a+bi$: $|12-5i|=\sqrt{12^{2}+(-5)^{2}}=\sqrt{144+25}=\sqrt{169}=13$