Random Questions from 2016 Prelims #11

TPJC/P2/4

(a) The complex number w is given by $3+3\sqrt{3}i$
(i) Find the modulus and argument of w, giving your answer in exact form.
(ii) Without using a calculator, find the smallest positive integer value of n for which $(\frac{w^3}{w^*})^n$ is a real number.

(b) The complex number z is such that $z^5 = - 4 \sqrt{2}$
(i) Find the value of z in the form $re^{i\theta}$ , where $r > 0$ and $- \pi \textless \theta \le \pi$ .
(ii) Show the roots on an argand diagram.
(iii) The roots represented by $z_1$ and $z_2$ are such that $0 \textless arg({z_1}) \textless arg({z_2}) \textless \pi$ . The locus of all points z such that $|z - z_1| = |z-z_2|$ intersects the line segment joining points representing $z_1$ and $z_2$ at the point P. P represents the complex number p. Find, in exact form, the modulus and argument of p.

Solution

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KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for almost two decades. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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Random Questions from 2016 Prelims #11

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Random Questions from 2016 Prelims #11

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