All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.




\frac{1}{z^{3}}=\frac{1}{-11-2i}\times \frac{-11+2i}{-11+2i}



Using (i)

Since it is real, 4p+\frac{2q}{125}=0

We have q=-250p,


Personal Comments:
(i) tests students on their understanding of manipulation and also how to rationalise a complex number. I strongly encourage students to still use the calculator to check their answers.
(ii) is quite comfortable so long as students realise the meaning of being real.

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