VCE Specialist 3/4 Question Thread!

[deStudent]

(Image removed from quote.)

The quadrilateral formed with the dotted lines (from the centre of the circle) and the tangents PA and PB.

2: lengths are only diameters when they are going through the centre of the circle.

True, thanks.

[Gogo14]

dont understand anything after line 3 can someone explain step by step what happens?

[wyzard]

dont understand anything after line 3 can someone explain step by step what happens?

A complex number multiplied by its own conjugate will give you its modulus squared.

For the middle bit, you'll can show it yourself separately by writing the complex number in Cartesian form.

[RuiAce]

dont understand anything after line 3 can someone explain step by step what happens?

[excelsiorxlcr]

Hi This may be a really dumb question but how do you factorise z cubed - (2 - i)z squared + z - 2 + i into linear factors over C?

Similarly, how do you solve the following over C:
z squared + (1 + 2i)z + (-1 + i) = 0 and z squared + z + (1 - i) = 0

Thanks!

[RuiAce]

Hi This may be a really dumb question but how do you factorise z cubed - (2 - i)z squared + z - 2 + i into linear factors over C?

Similarly, how do you solve the following over C:
z squared + (1 + 2i)z + (-1 + i) = 0 and z squared + z + (1 - i) = 0

Thanks!

Last two can be done by quadratic formula.

[deStudent]

For these 2 pictures http://m.imgur.com/a/dPo6l, this isn't the same question but they use same method but don't follow the same thinking to solve their respective questions. This has left me pretty confused.

For example, for picture 2 at line: "if x < 5/2”, wouldn't both of the moduluses be negative, therefore the line should be " -(2x-5) - (-4+x) = 10” (multiplied by -1) instead of what is written?

This is the logic I used to solve the question in the first image which ended up being correct, but using this logic for the 2nd image would've gotten me the wrong answer. Why is that?

Again, in the 2nd image, if x >= 4, this means both moduluses are positive. But they still multiplied (4-x) by -1, however this still got them the correct answer? In image 1, for x >=4, I took them both as a positive and solved. This gave me the correct answer for this question, but wouldn't of in the 2nd image.

Sorry if what I'm saying is unclear, I'm not sure how to say what I want to say concisely..

[RuiAce]

For these 2 pictures http://m.imgur.com/a/dPo6l, this isn't the same question but they use same method but don't follow the same thinking to solve their respective questions. This has left me pretty confused.

For example, for picture 2 at line: "if x < 5/2”, wouldn't both of the moduluses be negative, therefore the line should be " -(2x-5) - (-4+x) = 10” (multiplied by -1) instead of what is written?

This is the logic I used to solve the question in the first image which ended up being correct, but using this logic for the 2nd image would've gotten me the wrong answer. Why is that?

Again, in the 2nd image, if x >= 4, this means both moduluses are positive. But they still multiplied (4-x) by -1, however this still got them the correct answer? In image 1, for x >=4, I took them both as a positive and solved. This gave me the correct answer for this question, but wouldn't of in the 2nd image.

Sorry if what I'm saying is unclear, I'm not sure how to say what I want to say concisely..

Your fault was in that you got confused between |4-x| with the equivalent |x-4| in your working out.

|2x-5| - |4-x| = 10 is actually |2x-5| - |x-4| = 10

When x < 5/2 we have

-(2x-5) - (-(x-4)) = 10
______________________________

[excelsiorxlcr]

P193 question 5) Find the solutions of the equation z^4 - 2z^2 + 4 = 0 in polar form

Thanks!

[excelsiorxlcr]

Hi! I have another question - for complex numbers, when you have to graph stuff on argand diagrams, what do the inequalities actually mean? Eg: What does |z - 2| < 1 mean? Does it mean that the distance between (2, 0) and the outer edge of the circle is less than one?

[RuiAce]

P193 question 5) Find the solutions of the equation z^4 - 2z^2 + 4 = 0 in polar form

Thanks!

[RuiAce]

Hi! I have another question - for complex numbers, when you have to graph stuff on argand diagrams, what do the inequalities actually mean? Eg: What does |z - 2| < 1 mean? Does it mean that the distance between (2, 0) and the outer edge of the circle is less than one?

Short answer: Yes.

[deStudent]

http://m.imgur.com/a/cdk14

I don't understand the answer, the part about symmetry. How does that tell us a = 1?

Thx

[RuiAce]

http://m.imgur.com/a/cdk14

I don't understand the answer, the part about symmetry. How does that tell us a = 1?

Thx

[Syndicate]

http://m.imgur.com/a/cdk14

I don't understand the answer, the part about symmetry. How does that tell us a = 1?

Thx

Find the distance half way through 3 and -1 to get a (this would work, as this function is symmetric) .