2: Argand Diagrams

Question 1

Formula for |z|?

Answer 1

sqrt(x^2 + y^2)

Question 2

For number x+iy find θ?
(all 4 quadrants please)

Answer 2

tanθ = y/x
1: arg z = θ
2: arg z = π - θ
3: arg z = -(π - θ)
4: arg z = -θ

Question 3

Modulus-Argument form of z?

Answer 3

z = r(cosθ + isinθ)
where arg z = θ and |z| = r

Question 4

|z * w| can be rewritten as what?
|z/w| as well?

Answer 4

|z||w|

|z|/|w|

Question 5

arg(z * w) can be rewritten as what?
arg(z/w) as well?

Answer 5

arg z + arg w

arg z - arg w

Question 6

Given w = x + iy, what is the locust of a circle?

Answer 6

|z - w| = r or
|z - (x+iy)| = r
With centre (x,y) radius r

Question 7

Given w = x + iy and v = a + ib, what is the Perpendicular bisector or the line connecting the 2?

Answer 7

|z - w| = |z - v|

Question 8

Given w = x + iy, what is the locust of the half line from w making an angle(θ) with the line parallel to the x axis?

Answer 8

arg(z - w) = θ