The complex number p is given by p=(-1+i)(3+i). Give all arguments as principal arguments in radians

Question

The complex number p is given by p=(-1+i)(3+i). Give all arguments as principal arguments in radians. - Express p in Cartesian form. - Find the exact modulus and principal argument of p. - Hence show that tan(11pi)/(12)= 3-2.

Accepted Answer

(a) $p=-(\sqrt3+1)+(\sqrt3-1)i$ (b) $|p|=2\sqrt2,\ \arg p=\frac{11\pi}{12}$ (c) $\tan\frac{11\pi}{12}=\sqrt3-2$

A product with a second-quadrant argument

A product with a second-quadrant argument

Solution:

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