write 2-2i in its modulus argument form

firsly sketch out the 2-2i on an argand diagrm and draw a line from (0,0) to (2,-2). With the shortest distance Mark the angle theta from the positive x-axis to the line to see whether the argument is positive or negative.

then do arctan(-2/2) to get the angle -pi/4. notice this angle is from the neative x-axis to the point (2,-2) so have to do pi-pi/4 to get the argument 3pi/4.

the to get the modulus it's sqrt(2²+(-2²)) which is root(8)