Question

what is the argument of (2- 2i)?​

Answer 1

Answer:

HEY Buddy here's ur answer

The argument of -2 -2i is either the negative angle from the positive real axis clockwise to the radial line, or the positive angle from the positive real axis counterclockwise to the radial line.

Answer 2

$\huge{\underline{\underline{\mathtt{\purple{To\:Find}}}}}$

⇝ ${\mathtt{Argument\: of \: 2 \: - \: 2i}}$

$\huge{\underline{\underline{\mathtt{\purple{Solution}}}}}$

⇝ ${\mathtt{Let \:Z\: = \:2 \:- \:2i }}$

⇝ ${\mathtt{And\: Let \: \alpha \: be\: the\: acute \: angle }}$

⇝ ${\mathtt{Where\: \alpha\: is\: given \: by \: \implies }}$

${ \mathtt {\tan( \alpha ) \: = \: | \frac{ {Im(z)} }{Re(z)} | }}$

⇝${\mathtt{Now\: let \: us \: find \: the \: value\: of\: tan \: \alpha}}$

$\mathtt{\implies \: \tan( \alpha ) \: = \: | \frac{ - 2}{2} | = 1 }$

$\mathtt{\implies \: ( \alpha ) \: = \: \frac{\pi}{4} }$

⇝ ${\mathtt{Now\: from\: here \:we \:observed\: from \:the\: number \:that }}$

$\mathtt{Re(z) \: > \: 0 \: and \: Im(z) \: < \: 0}$

⇝ ${\mathtt{ So \:the \:point\: representing \:z\: lies \:in \:the \:fourth \:quadrant}}$

$\implies \: \mathtt{If \: point \: belongs \: to \: 4th\: quadrant \: then \: arg(z) \: = \: ( - \: \alpha}$

${ \mathtt{ \red { \: arg \: (z) \: = \: (\: - \: \frac{\pi}{4}) \: = \: -\:\frac{\pi}{4}\:}}}$

${\mathtt{Some \: Questions \: for \: self \: practice }}$

⇝ 1 + i√3

⇝ 2√3 - 2i

⇝-√3 - i

${\mathtt{Important\: points }}$

⇝ If point is in first quadrant then argument is equals to alpha .

⇝ If point belongs to second quadrant then argument is equals π - alpha

⇝If point belongs to 3rd quadrant then argument is equals to -( π - alpha )