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Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread how do you sketch y = -1/2 ( x^2 + 1) ??

Re: HSC 2016 4U Marathon Understand you clear explanation but just don't get this part: we can invert the expression in the arg to negate this angle to get pi/3

Re: HSC 2016 4U Marathon arg( (z-3)/(z+3) ) = +_ 5pi/3 What is the angle at the circumference. The answer say it is pi/3 , but why is that??

Re: HSC 2016 4U Marathon why is arg( (z)^1/2) = 1/2 arg z

Re: HSC 2016 4U Marathon determine the arcs specified by the following eqn. Sketch each one, showing the centre and radius of the associated circle. arg ( z - 1 + i) / (z - 1 - i ) = pi/2 So i know it a circle. there are endpoints at (1, -1 ) and ( 1, 1) and that there are not included ...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread determine the arcs specified by the following eqn. Sketch each one, showing the centre and radius of the associated circle. arg ( z - 1 + i) / (z - 1 - i ) = pi/2 So i know it a circle. there are endpoints at (1, -1 ) and (...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Two points P and Q where p > q, move along the parabola x^2 = 4ay . At all times the x cordinates of P and Q differ by 2a. Find the midpoint of the chord PQ. M ( a(p + q), 1/2 a(p^2 + q^2)) Now how do i find the...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread P (2ap, ap^2) and Q (2aq,aq^2) are points on x^2 = 4ay , and he chord PQ subtends a right angle at the vertex O. Show that pq = -4 It's probably really simple but I can't seem to work it out!

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread how would you check for restrictions??

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread For a question, when one of the parametric equation is a constant , why does the locus equal this constant??

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread If z1 and z2 are complex numbers such that | z1| = |z2|, show that: arg(z1z2) = arg((z1 + z2)^2))

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Thanks I get it now

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I understand your logic. But can you use the information that the vector joining z 1 to z2 is the same length as vector z2 to z3. I.E. using the fact that triangle is equilateral ( equal sides) when you are asked to SHOW ??

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread A triangle in the Argand diagram has vertices at the points representing the complex numbers z1,z2,z3. If (z2 - z1) / (z3 - z1) = cos ( pi/3) + isin (pi/3) , show that the triangle is equilaterial.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Cheers i understand

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread I only see two possible solution, using the two opposites sides that are equal and equating to find z4. Not sure about a third.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread How would you solve: Given that z1 = 1 + i , z2 = 2 + 6i , z3 = -1 + 7i , find the three possible values of z4 so that the points representing z1, z2, z3 and z4 form a parallelogram.

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Cheers I worked it out

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Answers are 1 - 5i, and 7 + 3i

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Can't you just multiply the point z1 by i. Why is this wrong???