in part two of our lesson on the trig form of complex numbers you will learn how to convert from rectangular form to trig form in this example, we have to express in complex trig form z is equal to two radical three minus 2i so let's first graph this number in the complex coordinate plane we know that the x value is two radical three, so that's a positive and the y value is -2 so that means our vector goes here this will be r and this will be theta using our conversion factors we know that r is equal to the square root of x squared plus y squared so that will be the square root of two radical three squared plus a -2 squared which is equal to the square root we know that two radical three squared becomes four times three which is 12 plus -2 squared is four this is the square root of 16 which is four, so we know r is four the tangent of theta is equal to y over x so in our case that is -2 divided by two radical three which is equal to -1 over radical three which we can ratio...