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Find the modulus and argument of each complex number and express it in the polar form. (1 + √3)/2

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Let z = \(\frac{1+\sqrt3}2=\frac12+\frac{\sqrt3}2i\)

\(\therefore\) a = \(\frac12\), b = \(\frac{\sqrt3}2\), a, b > 0

\(\therefore\) |z| = r = \(\sqrt{a^2+b^2}\)

Here, \((\frac12,\frac{\sqrt3}2)\) lies in 1st quadrant.

\(\therefore\) θ = amp(z) = tan-1(\(\frac{b}a\))

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