PPQ Corrections 2

Question 1

Inconsistency

Answer 1

0 0 0 I x

Question 2

Polar Form

Answer 2

r(cosθ+isinθ)

Question 3

Cartesian Form

Answer 3

x+iy

Question 4

argument

Answer 4

θ=tan-1(y/x)

Question 5

modulus

Answer 5

r=√x^2+y^2

Question 6

Counterexample proof

Answer 6

Prove that the opposite is true/false.

Question 7

Anticlockwise matrix rotation

Answer 7

( 1 , 0 ) = ( cosθ -sinθ)
( 0 , 1 ) ( sinθ cosθ)

Question 8

Clockwise matrix rotation

Answer 8

( 1 , 0 ) = ( cosθ sinθ)
( 0 , 1 ) ( -sinθ cosθ)

Question 9

Special Common Forms

Answer 9

∫ Top of fraction derivative of bottom = ln If(x)I + c
∫ f’(x) . f(x) .dx = 1/2 (f(x))^2 + c

Question 10

First Order Linear Differential Equations General Form

Answer 10

(dy/dx + P(x)y) e^∫P(x)dx = d/dx(ye^∫P(x)dx)

Question 11

First Order Linear Differential Equations Steps

Answer 11

1. Identify P(x) and integrate
2. Find I.F (e^∫P(x)dx)
3. Multiply both sides by I.F
4. Make LHS d/dx(ye^∫P(x)dx)