Question

Write the trigonometric forms of the complex numbers.

(3+i)(1+i)(\sqrt3+i)(1+i)

Solution

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a) The absolute value for a+bi=3+ia+bi = \sqrt 3 + i is the distance of (a,b)(a,b) from the origin:

r1=a2+b2=(3)2+12=2\begin{aligned} r_1 &= \sqrt {a^2 + b^2 } \\ &= \sqrt {(\sqrt 3)^2 + 1^2 } \\ &= 2 \end{aligned}

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