FP2

Serendreamers

Could someone explain to me parts 'a' and 'c' to me please?

a) is pretty obvious from the diagram and the text and c) follows from b).

Show some working.

Reply 2

2710

Original post by Serendreamers

Could someone explain to me parts 'a' and 'c' to me please?

for a, draw 2 rectangles.

Make one rectangle using the line Z2 as a diagonal, and another with Z1. With angles and Z1=Z2, you can determine the answer

Reply 3

Serendreamers

Original post by 2710

for a, draw 2 rectangles.

Make one rectangle using the line Z2 as a diagonal, and another with Z1. With angles and Z1=Z2, you can determine the answer

Hello

I'm still really confused as to why z1=iz2

Reply 4

2710

Original post by Serendreamers

Hello

I'm still really confused as to why z1=iz2

Did you draw the rectangles? Let arg(Z1) = x degrees say. Now try and label every other angle of the rectangle according to x.

Reply 5

Serendreamers

Original post by 2710

Did you draw the rectangles? Let arg(Z1) = x degrees say. Now try and label every other angle of the rectangle according to x.

Is it simply that,

z2 = z1 * cis(pi/2)
z2 = i z1

???

Reply 6

2710

I have attached a picture

Untitled.png29.7KB

Reply 7

2710

Original post by Serendreamers

Is it simply that,

z2 = z1 * cis(pi/2)
z2 = i z1

???

In my picture, tell me what y and k are, in terms of x. And then what can you tell me about the triangles

Reply 8

Serendreamers

Original post by 2710

In my picture, tell me what y and k are, in terms of x. And then what can you tell me about the triangles

k=x, y=(pi/2)-x and the triangles are congruent

Reply 9

2710

Original post by Serendreamers

k=x, y=(pi/2)-x and the triangles are congruent

Yes, can you see where to go from there?

Reply 10

Serendreamers

Original post by 2710

Yes, can you see where to go from there?

So, from the triangles and their angles, I can deduce that

z1 = a+bi and z2 = -b+ai

which confirms with the statement

iz1 = i(a+bi) = -b+ai = z2

Is this it?

Reply 11

2710

Original post by Serendreamers

So, from the triangles and their angles, I can deduce that

z1 = a+bi and z2 = -b+ai

which confirms with the statement

iz1 = i(a+bi) = -b+ai = z2

Is this it?

yes

Reply 12

Serendreamers

Original post by 2710

yes

Well, I have already thought of this as a solution but the mark scheme surprisingly did not give me 2/2 marks for this explanation

Is there another reason why iz1=z2? Unfortunately, the mark scheme isn't very helpful...

Untitled.png3.1KB

Reply 13

aznkid66

Original post by Serendreamers

Is it simply that,

z2 = z1 * cis(pi/2)
z2 = i z1

???

Did the markscheme not reward this?

Reply 14

Serendreamers

Original post by aznkid66

Did the markscheme not reward this?

See my above post, it simply states 'Explantion' implying that the answer is very obvious

Reply 15

aznkid66

Original post by Serendreamers

See my above post, it simply states 'Explantion' implying that the answer is very obvious

Sorry, I missed that.

Anyway, I don't see what the problem is. The mark scheme rewards partials for both adding the angles and using congruent components, so either method written out fully should be sufficient. What do you mean by "the mark scheme did not give [you] 2/2 marks"?

Reply 16

Serendreamers

Original post by aznkid66

Don't worry about it, I just got a bit confused :biggrin:

Do you have any idea for part 'c'?

Reply 17

aznkid66

I'm confused about "in terms of z1", but it should follow from the diagram you drew.

Do you know where else the perpendicular bisector of an isosceles triangle's unique side intersects the triangle?