Complex numbers are turns and stretches — and their roots are stars on a circle.
Eight instrument plates for the Leaving Cert HL complex-numbers strand. Watch each idea draw itself from real arithmetic, drag the numbers to feel the rules, then chart the roots yourself.
+2πk FIRST, then ÷ n
w doesn’t care how many whole turns you took to reach it. Add 2πk before dividing by n, and k = 0…n−1 hands you all n roots — forget it and you’ll find only one.
ROOT the modulus · DIVIDE the argument
The modulus takes the n-th root: ⁿ√R. The argument gets divided by n. Swap those two jobs and every root lands on the wrong circle.