Core Pure

Question 1

Equation of Circle in Argand Diagram

Answer 1

|z - (a + bi)| = r

Question 2

Equation of Half Line in Argand Diagram

Answer 2

Arg(z - (a + bi)) = θ

Question 3

Equation of Perpendicular Bisector in Argand Diagram

Answer 3

|z - (a + bi)| = |z - (c + di)|

Question 4

Gradient of Half Line: Arg(z) = θ

Answer 4

tan(θ)

Question 5

How many Radians in one full turn?

Answer 5

2π

Question 6

Modulus Argument Form

Answer 6

z = r (cosθ + i sinθ)

where r = |z|, θ = Arg(z)

Question 7

Let z = a + bi,

What is the name and value of z*?

Answer 7

Complex Conjugate

a - bi

Question 8

Quadratic Formula

Answer 8

(-b ± sqrt(b^2 - 4ac)) / 2a

Question 9

Let z = a + bi

What are the values of Re(z) and Im(z)?

Answer 9

Re(z) = a
Im(z) = b

Question 10

Let z = a + bi

What is the name and value of |z|?

Answer 10

Modulus, distance from Origin to z

sqrt(a^2 + b^2)

Question 11

Let z = a + bi

What is the name and value of Arg(z)?

Answer 11

Argument, angle between Real axis and line to z from Origin

tan^-1 (b / a)

Question 12

What are the values of |z| x |w| and |z| + |w|?

Answer 12

|z| x |w| = |zw|

|z| + |w| = |z| + |w| (doesn’t simplify)

Question 13

What are the values of Arg(z) x Arg(w) and Arg(z) + Arg(w)?

Answer 13

Arg(z) x Arg(w) = Arg(z) x Arg(w) (doesn’t simplify)

Arg(z) + Arg(w) = Arg(zw)

Question 14

First step for square rooting a complex number? e.g. 2 + 3i

Answer 14

Set sqrt(2 + 3i) equal to a + bi,
2 + 3i = (a + bi)^2 = a^2 + 2abi + b^2

Question 15

What translation is represented by:
( 1 a )
( 0 1 )

Answer 15

Shear, x axis fixed, (0, 1) maps to (a, 1)

Question 16

What translation is represented by:
( 1 0 )
( a 1 )

Answer 16

Shear, y axis fixed, (1, 0) maps to (1, a)

Question 17

What is the General Rotation Matrix?

Answer 17

( cosθ -sinθ )

sinθ cosθ

Question 18

What Matrix represents:
( 0 1 ) ( -1 0 )
( 1 0 ) followed by ( 0 1 )

Answer 18

( -1 0 )    ( 0 1 ) 
( 0  1 ) x ( 1 0 )
=
( 0 -1 )
( 1  0 )