If z -2-1- i -3- then the value of z isA- -B- -3C- 2 -3D- -4

The correct option is C 2π/3 z= 2/1+i√(3) Rationalising z, we get, z= 2/1+i√(3)×1 i√(3)/1 i√(3) ⇒ z= 2+i2√(3)/1+3 ⇒ z= 1+i√(3)/2⇒ z= 1/2+i√(3)/2 tan α =|Im(z ...

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Byju's Answer

Standard XII

Mathematics

Argument of a Complex Number

If z =-2/1+ i...

Question

If $z = \frac{- 2}{1 + i \sqrt{3}}$ , then the value of arg(z) is

$π$

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$\frac{π}{3}$

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$\frac{2 π}{3}$

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$\frac{π}{4}$

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Solution

The correct option is C
$\frac{2 π}{3}$

$z = \frac{- 2}{1 + i \sqrt{3}} Rationalising z, we get, z = \frac{- 2}{1 + i \sqrt{3}} \times \frac{1 - i \sqrt{3}}{1 - i \sqrt{3}} \Rightarrow z = \frac{- 2 + i 2 \sqrt{3}}{1 + 3} \Rightarrow z = \frac{- 1 + i \sqrt{3}}{2} \Rightarrow z = \frac{- 1}{2} + \frac{i \sqrt{3}}{2} t a n α = ∣ ∣ \frac{I m (z)}{R e (z)} ∣ ∣ = \sqrt{3} \Rightarrow α = \frac{π}{3}$

Since, z lies in the second quadrant.

Therefore, arg (z) = $π - \frac{π}{3} = \frac{2 π}{3}$

Suggest Corrections

If z=−21+i√3, then the value of arg(z) is

The correct option is C 2π3 z=−21+i√3Rationalising z, we get,z=−21+i√3×1−i√31−i√3⇒ z=−2+i2√31+3⇒ z=−1+i√32⇒ z=−12+i√32tan α =∣∣Im(z)Re(z)∣∣=√3⇒ α=π3 Since, z lies in the second quadrant. Therefore, arg (z) = π−π3=2π3

If $z = \frac{- 2}{1 + i \sqrt{3}}$ , then the value of arg(z) is