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HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 2 => Topic started by: mani.s_ on February 28, 2020, 10:01:07 am

Title: Faster way to solve square roots of complex numbers?
Post by: mani.s_ on February 28, 2020, 10:01:07 am: Hi, I recently saw a much faster way to solve the square root of complex numbers, the traditional method being letting the square root equal another complex number, squaring both sides and equating the parts.

This is the new method:

Say we have a complex number: $z=\sqrt{a+ib}$ We let this complex number equal another complex number: $x+iy$ Then:

$z=\sqrt{a+ib}=x+iy$
$x^2=\frac{|z|+a}{2}, y^2=\frac{|z|-a}{2}$
$x^2=\frac{\sqrt{a^2+b^2}+a}{2}, y^2=\frac{\sqrt{a^2+b^2}-a}{2}$

We then just find our x and y, and the sign between them is the sign in the original sqare root complex number (+) or (-).

If I were use this method in the HSC, is there a possibility of me losing marks?
Title: Re: Faster way to solve square roots of complex numbers?
Post by: RuiAce on February 28, 2020, 01:56:16 pm: Quote from: mani.s_ on February 28, 2020, 10:01:07 am
$z=\sqrt{a+ib}=x+iy$
$x^2=\frac{|z|+a}{2}, y^2=\frac{|z|-a}{2}$
I can't see why this jump here is immediately obvious?
Title: Re: Faster way to solve square roots of complex numbers?
Post by: mani.s_ on February 28, 2020, 02:25:47 pm: Quote from: RuiAce on February 28, 2020, 01:56:16 pm
I can't see why this jump here is immediately obvious?
Its really not, I saw this online and its a faster way to solve square roots for complexes. The best thing is that it works. I was wondering whether Ill be allowed to use this in the HSC or school?
Title: Re: Faster way to solve square roots of complex numbers?
Post by: RuiAce on February 28, 2020, 02:29:01 pm: Quote from: mani.s_ on February 28, 2020, 02:25:47 pm
Its really not, I saw this online and its a faster way to solve square roots for complexes. The best thing is that it works. I was wondering whether Ill be allowed to use this in the HSC or school?
The HSC examines the procedure of finding square roots. Use of the actual square-root formula will instantly cost you marks.
Title: Re: Faster way to solve square roots of complex numbers?
Post by: mani.s_ on February 28, 2020, 02:33:12 pm: Quote from: RuiAce on February 28, 2020, 02:29:01 pm
The HSC examines the procedure of finding square roots. Use of the actual square-root formula will instantly cost you marks.
ahhh ok, thank you so much!