Rose’s method for getting exact answers with Pol( , ) and Rec( , )

calcul

You want to find the modulus (the “r”) and the argument (the “θ”) of, for example, (1,1).

complex

You enter Pol(1,1) on your calculator and get (if the calculator is set to radians)

r=1.414213562, θ=0.7853981634

Ok, but you want the answers exactly, as surds or fractions of π

Press the “Alpha” key (top left of the calculator)

Press X=, and you get √2, which is the exact value for r

Press Y=, and you get ¼π, which is the exact value for θ

cuberoots

You can do the same sort of thing with Rec( , )

You want to find all the cube roots of 64, and you have them as

4 cis 0 (which is just 4)

4 cis 120

and 4 cis 240

You want to find 4 cis 120 and 4 cis 240 in x+iy form

Key in Rec(4,120) with your calculator set to work in degrees

You get X=−2, Y=3.464101615

and you want the exact answer in surds

Press Alpha and Y=, and you get

Y=2√3

Thanks for all this to Rose Hemans!