Complex numbers

Question 1

|z|

Answer 1

|z| = √x^2 + y^2

Question 2

z1z2

Answer 2

r1r2(cos(Θ1+Θ2) + i sin(Θ1+Θ2))

Question 3

z1/z2

Answer 3

r1/r2(cos(Θ1-Θ2) + i sin(Θ1-Θ2))

Question 4

tanΘ from complex to polar coords

Answer 4

tanΘ = b/a

Question 5

r from complex to polar coords

Answer 5

r = |z| = √x^2 + y^2

Question 6

z^n

de moivre’s theorem

Answer 6

r^n(cos(nΘ) + i sin(nΘ))