argand diagrams

Question 1

What is one radian?

Answer 1

The measurement of an angle subtended by an arc of length r

Question 2

How many radians in 360°?

Answer 2

2π

Question 3

How many radians in 180°?

Answer 3

π

Question 4

How many radians in 90°?

Answer 4

π/2

Question 5

How many radians in 45°?

Answer 5

π/4

Question 6

How many radians in 60°?

Answer 6

π/3

Question 7

How many radians in 30°?

Answer 7

π/6

Question 8

How many radians in 270°?

Answer 8

3π/2

Question 9

How are complex numbers represented on Argand diagrams?

Answer 9

z=x+iy = (x,y)

Question 10

What do complex conjugate pairs look like on Argand diagrams?

Answer 10

Reflections of each other in the x-axis

Question 11

What happens when two points are added together on an Argand diagram?

Answer 11

The resulting complex number forms a parallelogram with the two added complex numbers and (0,0)

Question 12

What is the modulus of a complex number?

Answer 12

The magnitude of its corresponding vector

Question 13

How is the modulus calculated?

Answer 13

|z| = ✔️(x^2 + y^2)

Question 14

What is the argument of a complex number? (2)

Answer 14

The angle (θ) that the vector makes with the positive real axis
Usually given in the range -π < θ ≤ π (principal argument)

Question 15

What is the modulus-argument form of a complex number?

Answer 15

z = r(cos(θ) +i sin(θ)) where r is the modulus and theta is the argument