For some practice working with complex numbers: Calculate (3-4i)+(2+5i) = , (3-4i)-(2+5i) = , (3-4i)(2+5i) = . The complex conjugate of (1+i) is (1-i). In general to obtain the complex conjugate reverse the sign of the imaginary part. (Geometrically this corresponds to finding the “mirror image” point in the complex plane by reflecting through the x-axis. The complex conjugate of a complex number z is written with a bar over it: z?? and read as “z bar”. Notice that if z=a+ib, then (z)(z??)=|z|2=a2+b2 which is also the square of the distance of the point z from the origin. (Plot z as a point in the “complex” plane in order to see this.) If z=3-4i then z?? = and |z| = . You can use this to simplify complex fractions. Multiply the numerator and denominator by the complex conjugate of the denominator to make the denominator real. (3-4i)/(2+5i)= +i . Two convenient functions to know about pick out the real and imaginary parts of a complex number. Re(a+ib)=a (the real part (coordinate) of the complex number), and Im(a+ib)=b (the imaginary part (coordinate) of the complex number. Re and Im are linear functions — now that you know about linear behavior you may start noticing it often.