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[shaon0]

Hey guys, i need help with the following questions.
Question 1 d)
Question 2 bii)--> do i just use binomial theorem to expand it then equate the reals and unreals, this seems very time consuming.
Question 2 c)--> i ended up getting a circle with the centre at (1,0) and radius of 1 units. Is this right?

 

[Trebla]

Q1d)
Rewrite x as - (1 - x - 1)
So: - (1 - x - 1) / √(1 - x) = - √(1 - x) + 1/√(1 - x)
which becomes a simple integral
You could also use the substitution u = 1 - x or u² = 1 - x

Q2b)ii)
There is no need to use binomial theorem. Just apply De Moivre's theorem and evaluate the trig functions. You should get 256 + 256i

Q2c)
That's almost correct. The origin (z = 0) is excluded from the locus, because the denominator cannot be zero.

 

[shaon0]

Q1d)
Rewrite x as - (1 - x - 1)
So: - (1 - x - 1) / √(1 - x) = - √(1 - x) + 1/√(1 - x)
which becomes a simple integral
You could also use the substitution u = 1 - x or u² = 1 - x

Q2b)ii)
There is no need to use binomial theorem. Just apply De Moivre's theorem and evaluate the trig functions. You should get 256 + 256i

Q2c)
That's almost correct. The origin (z = 0) is excluded from the locus, because the denominator cannot be zero.

Thanks for your help