Question

find modulus and argument of 2√3-2i

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: given \: complex \: number \: is \\ 2 \sqrt{3} - 2i \\ \\ comparing \: it \: with \: a + ib \\ we \: get \\ \\ a = 2 \sqrt{3} \\ b = - 2 \\ \\ so \: we \: know \: that \\ \\ |z| = \sqrt{a {}^{2} + b {}^{2} } \\ \\ = \sqrt{( 2\sqrt{3} ) {}^{2} + ( - 2) {}^{2} } \\ \\ = \sqrt{12 + 4} \\ \\ = \sqrt{16} \\ \\ |z| = 4$

$so \: thus \: then \\ \\ arg \: (z) = tan \: θ = \frac{b}{a} \\ \\ = \frac{ - 2}{2 \sqrt{3} } \\ \\ = \frac{ - 1}{ \sqrt{3} } \\ \\ so \: as \: here \: \\ \: (a,b) = (2 \sqrt{3} , - 2) \\ it \: lies \: in \: quadrant \: 4 \\ \\ hence \: then \: \\ \\ tan \: θ = 330 = \frac{11\pi {}^{c} }{6} \\ \\ therefore \\ \\ arg \: (z) = \frac{11\pi {}^{c} }{6}$