By inspection (1 Viewer)

[artosis]

Find the two square roots of −16 + 30i.

obviously the most popular method of doing this is by solving it with simultaneous equations, but that takes WAY longer. I can probably do this in 30secs with inspection method and probably takes like 2mins with simultaneous.
This is from Sydney Grammer's 2011 trial but ive seen it in a lot of other solutions.

So, does the method warrant full marks in the HSC?
these questions are worth 3 marks in the HSC. eg 2009 paper

 

[math man]

The HSC is generally nice when marking they wanna give you marks...i reckon just add one line in saying equating real and imaginary parts gives: then you should be fine, doing this extra line demonstrates to the marker you know what you are doing

 

[D94]

Yeah, by inspection is fine. I reckon it's more common than using simultaneous equations, because it's faster.

 

[Shadowdude]

The HSC is generally nice when marking they wanna give you marks...i reckon just add one line in saying equating real and imaginary parts gives: then you should be fine, doing this extra line demonstrates to the marker you know what you are doing

^ That.

Your second line should be: "Therefore, equating real and imaginary parts..."

 

[cutemouse]

these questions are worth 3 marks in the HSC. eg 2009 paper

You need to show working though. It said in the marker's comments that some students just wrote the answer without any working, and that doing so did not give full marks.

 

[D94]

You need to show working though. It said in the marker's comments that some students just wrote the answer without any working, and that doing so did not give full marks.

But that was because students only wrote +/-(2+i), but the above example has working out, and a development to show the marker the student knows what they are doing.

If you look at the official Sample Answers, even they have used the inspection method.

 

[artosis]

^ thanks for that. big sigh of relief that the hsc markers do it as well.

they dont even right "by comparing real and imaginary parts..." or "by inspection..."
they're really lazy
they only did like, 2 lines of working for a 3 mark question. (disregard 1st line and last line since its not any working out)

 

[largarithmic]

Surely the way to do it would be, in the question you linked (and the way I did it in that exam):

"By inspection, z = 3+5i and -3-5i satisfy the equation z^2 = -16 + 30i. Since this equation, a quadratic, has at most two roots, 3+5i and -3-5i are the complete set of square roots of -16+30i"