# MX2 Marathon (1 Viewer)

#### dan964

##### what
Welcome to the 2018 Maths Ext 2 Marathon

Post any questions within the scope and level of Mathematics Extension 2. Once a question is posted, it needs to be answered before the next question is raised.
This thread is mainly targeting Q1-15 difficulty in the HSC.

Q16/Q16+ material to be posted here:

I encourage all current HSC students in particular to participate in this marathon.

Have fun ^_^

http://community.boredofstudies.org/14/mathematics-extension-2/361256/maths-ext-2-resource-list.html

#### Sy123

##### This too shall pass
Re: HSC 2018 MX2 Marathon

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#### TheZhangarang

##### New Member
Re: HSC 2018 MX2 Marathon

i) x^2+y^2=1

ii) x^2+(y-im(z))^2=1

I've probably misinterpreted the question given it does seem overly simple

#### Sy123

##### This too shall pass
Re: HSC 2018 MX2 Marathon

i) x^2+y^2=1

ii) x^2+(y-im(z))^2=1

I've probably misinterpreted the question given it does seem overly simple
I made a typo in writing the first question, it should be fixed now. Your second answer however has a 'z' there but this is not a proper cartesian equation for the locus, you want only 'x's and 'y's

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

if (x+iy)(a+ib) = b+ia, express x,y in terms of a,b
thank you!!

#### dan964

##### what
Re: HSC 2018 MX2 Marathon

if (x+iy)(a+ib) = b+ia, express x,y in terms of a,b
thank you!!
expand
(xa-by) +(ay+bx)i=b+ia
equate real and complex and solve simulataneously for x,y

• sssona09

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

expand
(xa-by) +(ay+bx)i=b+ia
equate real and complex and solve simulataneously for x,y
ohh thank you #### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

find x,y if
2z/(1+i) - 2z/i = 5/(2+i)

can't seem to get it,, do I sub x+iy later

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

You could if you want to. Rationalise denominator and then solve for it by equating real and imaginary parts
oh okay thanks #### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

E+ni is a root for ax2+bx+c=0
where a and b and c are real
show that an^2 =aE^2 + bE +c

so I figured that the other root is E-ni but I've tried using product of roots, but can't seem to prove this :/

#### 1729

##### Active Member
Re: HSC 2018 MX2 Marathon

E+ni is a root for ax2+bx+c=0
where a and b and c are real
show that an^2 =aE^2 + bE +c

so I figured that the other root is E-ni but I've tried using product of roots, but can't seem to prove this :/

• sssona09

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

Ahh thank you!!!!!!!!!!

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

how do i divide x^3-2-2i by x+1-i

#### Sp3ctre

##### Active Member
Re: HSC 2018 MX2 Marathon

how do i divide x^3-2-2i by x+1-i
It's the same as any long division, but just treat -2-2i and 1-i each as one term.

• sssona09

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

if cube root (x+iy) =X+iY show that 4 (X^2-Y^2) = x/X + y/Y

#### 1729

##### Active Member
Re: HSC 2018 MX2 Marathon

if cube root (x+iy) =X+iY show that 4 (X^2-Y^2) = x/X + y/Y

• sssona09

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

thank you so much!!

#### sssona09

##### Member
Re: HSC 2018 MX2 Marathon

rove by Induction that z1+z2+zn = z1 +z2 +zn

where the LHS has a big conjugate line on the top and RHS has small conjugate lines

edit: solved

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#### dan964

##### what
Re: HSC 2018 MX2 Marathon

rove by Induction that z1+z2+zn = z1 +z2 +zn

where the LHS has a big conjugate line on the top and RHS has small conjugate lines
Prove by Induction that
is this the question?