11-2

today im reteaching 11-2 which is complex numbers with polar and rectangular. the complex form of rectangular is z= x + yi. the complex form for polar is z= r cis (theta). you can also multiply these numbers and to do so for rectangular you would just do FOIL and get your answer. for polar you mulitply the r's and add the theta's. here is an example below.

EX:
express each complex number in polar form
1) -1 + i
you do same steps to convert from rectangular to polar.
(the square root of) (-1) ^2 + (1)^2 = (the square root of) 2
(theta) = tan (inverse) 1/-1
the quadrants that they are negative is 2nd and 4th
(theta) = tan (inverse) 45
convert to second and fourth quadrant
-45 +180= 135
-45 +360= 315
now you have to figure out which to use
(-1,1) is in second quadrant so you use 135
so your polar form is r cis (theta) = (the square root of) 2 cis 135 (degrees)