Random Questions from 2016 Prelims #11


(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.

Leave a Comment

one × five =

Contact Us

CONTACT US We would love to hear from you. Contact us, or simply hit our personal page for more contact information

Not readable? Change text. captcha txt

Start typing and press Enter to search