Square Roots of a Complex Number (1 Viewer)

[HSC2014]

Question: Find the square roots of -21 + 20i
My solution:
root (-21 +20 i ) = root [ (2)^2 + (5i)^2 + 2 (2) (5i) ]
= +- (2 + 5i)

Is this acceptable? My concerns involve the shortness of the solution. I expressed -21 + 20i as a perfect square (it is pretty clear to me) and so I am able to obtain the roots very quickly - but I don't know about markers. I don't like the method where i say x^2 - y^2 = -21, and 2xy = 20... etc. I know that is necessary sometimes but not for this question.

 

[Carrotsticks]

That is perfectly fine. For Trials/internal assessments, you may need to watch out.

But for the HSC, it's perfectly 'legal'.

 

[HSC2014]

Okay thanks Good to know... I don't want my pen to waste ink.