# Thread: HSC 2017 MX2 Marathon

1. ## Re: HSC 2017 MX2 Marathon

Not sure if its me or the book error but I had a complex number question

(6+i)(a+bi)=2

My solution for
$a= \frac{12}{37} \ and \ b =\frac{-2}{37}$

My book has a different solution to that.

2. ## Re: HSC 2017 MX2 Marathon

Originally Posted by davidgoes4wce
Not sure if its me or the book error but I had a complex number question

(6+i)(a+bi)=2

My solution for
$a= \frac{12}{37} \ and \ b =\frac{-2}{37}$

My book has a different solution to that.
I also got the same answer as you.

3. ## Re: HSC 2017 MX2 Marathon

I spent 5 minutes on this and couldn't solve it.

$By writing z=x+yi, solve the following equations:$

$z^2 = 5+i$

$Ans: \pm \sqrt{\frac{\sqrt{26}+5}{2}}+ i \sqrt{\frac{\sqrt{26}-5}{2}}$

4. ## Re: HSC 2017 MX2 Marathon

I think my book has done another mistake. (The book has made a few mistakes so I'm just checking with people on here)

5. ## Re: HSC 2017 MX2 Marathon

i got an

x+yi

my x-component was :

$x = \pm (\sqrt{{\frac{5}{4}}+\frac{\sqrt{26}}{2}})$

I haven't solved the y-component yet. Want to get 'x' right before I do the y.

6. ## Re: HSC 2017 MX2 Marathon

The book's answer is right, you can check it by squaring it to get 5 + i.

7. ## Re: HSC 2017 MX2 Marathon

Originally Posted by davidgoes4wce
I spent 5 minutes on this and couldn't solve it.

$By writing z=x+yi, solve the following equations:$

$z^2 = 5+i$

$Ans: \pm \sqrt{\frac{\sqrt{26}+5}{2}}+ i \sqrt{\frac{\sqrt{26}-5}{2}}$
x^2 - y^2 + 2xyi = 5+i

Comparing real and imaginary
2xy = 1
y = 1/2x

x^2 - y^2 = 5
x^2 - 1/4x^2 = 5
4x^4 - 20x^2 - 1 = 0
x^2 = (20 +- sqrt(20^2 - 4(4)(-1))/2(4)
x^2 = (20+- sqrt(416))/8
x^2 = (20 +- 4sqrt(26))/8
x^2 = (5 +- sqrt(26))/2

But x is real so take the positive case only
x = +- sqrt[(5+sqrt26)/2]

8. ## Re: HSC 2017 MX2 Marathon

Originally Posted by davidgoes4wce
I spent 5 minutes on this and couldn't solve it.

$By writing z=x+yi, solve the following equations:$

$z^2 = 5+i$

$Ans: \pm \sqrt{\frac{\sqrt{26}+5}{2}}+ i \sqrt{\frac{\sqrt{26}-5}{2}}$
http://i.imgur.com/xWfCJry.jpg

Page 5 of 5 First ... 345

There are currently 1 users browsing this thread. (0 members and 1 guests)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•