Mjc 2010 H2 Math Prelim File

Derivation: The triangle formed by cube roots of a complex number is equilateral, area formula (\frac3\sqrt34 R^2).

(a) Find the modulus and argument of (z^3), hence find the three roots of the equation in the form (r e^i\theta) where (r>0) and (-\pi < \theta \le \pi). Mjc 2010 H2 Math Prelim

The complex number (z) satisfies the equation [ z^3 = -8\sqrt2 + 8\sqrt2 i. ] Derivation: The triangle formed by cube roots of

Better: (16^1/3 = 2^4/3). But leave as (\sqrt[3]16 = 2\sqrt[3]2). 0) and (-\pi &lt

(c) Find the exact area of the triangle formed by these three roots.