square roots of complex numbers (1 Viewer)

[mr.habibbi]

Hi all,

Just want to check if i can use this formula to solve questions like this. Works every time and saved me a lot of working.

 

[Life'sHard]

Hi all,

Just want to check if i can use this formula to solve questions like this. Works every time and saved me a lot of working.
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Nope you can't. 3 marks are allocated for a reason. Otherwise it would just be 1 with that formula.

 

[Drongoski]

I like the method in Terry Lee's book: turn 15 - 8i into a square.

 

[quickoats]

This formula is quite difficult and easy to forget (kinda like the solution to a cubic). The complete the square method above is perfectly valid. The term i is your "2ab" term and figure the rest out accordingly.

 

[tito981]

im pretty sure you can state a=x^2-y^2 and b=2xy and then do it by inspection from there.

 

[mr.habibbi]

im pretty sure you can state a=x^2-y^2 and b=2xy and then do it by inspection from there.

inspection method will be much harder for fractional or square root values of a and b

 

[windebygirl]

Hi all,

Just want to check if i can use this formula to solve questions like this. Works every time and saved me a lot of working.
View attachment 31722
View attachment 31723

woah i did not know a formula for this existed. but honestly just doing it the normal way seems easier (at least for me) coz even tho it might be a little bit of working, it's quick and there's not much to it. it's an easy 3 marks. your formula seems risky, unless you're super confident in your formula memorising capability.

 

[mr.habibbi]

woah i did not know a formula for this existed. but honestly just doing it the normal way seems easier (at least for me) coz even tho it might be a little bit of working, it's quick and there's not much to it. it's an easy 3 marks. your formula seems risky, unless you're super confident in your formula memorising capability.

its actually much quicker n easier, some indian dude on yt explained it non verbally pretty well

 

[CM_Tutor]

@mr.habibbi, the problem is that the formula is not given in the syllabus and so you should justify that it is true before using it. Look at the answer @Drongoski used. Each step follows logically from the one before, and I can see no basis on which it can be faulted if the question was something like the one you posted.

Now, if a question specified a method, like

​

then Drongoski's method need modifying (as would your formula method).

You might get away with using the formula if finding the square root was simply a step in a larger problem and not specifically requested (in the same way that using a calculator might be acceptable) to simply assert the answer.

What you can use it for is to find the answer to check your working doesn't include an error.

 

[A1La5]

What I do is to take the modulus of both sides and to use:

to get an equation in terms of x^2 + y^2. The sign of the imaginary part is then used to determine the corresponding signs of and b. If Im(z) > 0, a and b will have the same sign. And if Im(z) < 0, then a and b will have opposite signs. This method is further outlined in the Cambridge textbook I believe..

 

[tito981]

im pretty sure you can state a=x^2-y^2 and b=2xy and then do it by inspection from there.

this is true, but the 'a' term will always be a fraction if either x or y is a fraction, if they are both fractions then you can tell via the 'b' term, so you can tell if you can use the inspection method instantly.

 

[mr.habibbi]

I like the method in Terry Lee's book: turn 15 - 8i into a square.

this question was in my 4u trial today, i used terry lee's inspection method using 1 line of working



will this get 3/3 ?

 

[Life'sHard]

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this question was in my 4u trial today, i used terry lee's inspection method using 1 line of working



will this get 3/3 ?

Depends how lenient your school is when marking. I'm pretty sure my school wouldn't have liked it done like that. I guess you could argue your own case. But I don't understand why you can't just do it the normal way of squaring both sides and then equating real and imaginary. It would just make more sense to hit those 3 marks. But idk 4u has many alternatives when solving.

 

[quickoats]

View attachment 31760

this question was in my 4u trial today, i used terry lee's inspection method using 1 line of working



will this get 3/3 ?

You were able to evidently show all steps clearly. The formula doesn’t.

 

[Drongoski]

View attachment 31760

this question was in my 4u trial today, i used terry lee's inspection method using 1 line of working



will this get 3/3 ?

Unless you are told to use another specific method, what's wrong or illegitimate about using "Terry Lee's" method. It's neat. It's very short. It's beautifully efficient. In fact it's cool.
Do you want to use the usual method, requiring 10 to 15 lines? But it's not necessarily easy to use the Terry Lee's method for all questions; but for exam style questions, it usually is.