TS EAMCET · Maths · Complex Number
If \(z=1+i \sqrt{3}\) then \(|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|\) is equal to
- A 0
- B \(\frac{\pi}{3}\)
- C \(\frac{\pi}{2}\)
- D \(\frac{2 \pi}{3}\)
Answer & Solution
Correct Answer
(D) \(\frac{2 \pi}{3}\)
Step-by-step Solution
Detailed explanation
\(z=1+i \sqrt{3}\) Let \(1+i \sqrt{3}=r(\cos \theta+i \sin \theta)\) Then, \(\quad r \cos \theta=1\) \(\ldots\) (i) \(r \sin \theta=\sqrt{3}\) \(\ldots\) (ii) Eq. (i) + Eq. (ii), we get \(r^2\left(\sin ^2 \theta+\cos ^2 \theta\right)=3+1\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The locus of the complex number \(z\) such that \(\arg \left(\frac{z-2}{z+2}\right)=\frac{\pi}{3}\)TS EAMCET 2011 Hard
- If , then isTS EAMCET 2018 Medium
- If \(S_1\) and \(S_2\) are the variances of the first \(2 k\) and \(k(k>1)\) natural numbers respectively, then \(\left(S_1 / S_2\right)\) lies in the intervalTS EAMCET 2020 Easy
- The angle between the pair of straight lines isTS EAMCET 2021 Easy
- The mid-point of the chord of the circle \(x^2+y^2-6 x+4 y-12=0\) drawn parallel to the tangent at \((-1,1)\) and at a distance of one unit from the tangent isTS EAMCET 2020 Hard
- \(\int_0^{\pi / 2} \frac{d x}{4+5 \sin x}\)TS EAMCET 2020 Hard
More PYQs from TS EAMCET
- is valid when lies in the intervalTS EAMCET 2021 Easy
- There are four bulbs of power \(100 \mathrm{~W}, 200 \mathrm{~W}\), \(500 \mathrm{~W}\) and 1000W. Among these whose filament has high resistance? (Assuming, same voltage source)TS EAMCET 2020 Easy
- Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(a x^2+b x+c=0\). Observe the lists given below
The correct match of List-I from List-II is (i) (ii) (iii) (iv)TS EAMCET 2008 Medium - If \(\int \frac{e^x-1}{e^x+1} d x=f(x)+c\), then \(f(x)\) is equal toTS EAMCET 2007 Medium
- The temperature at which the reading on Fahrenheit scale becomes \(90 \%\) more than the reading on Celsius scale isTS EAMCET 2025 Medium
- The objective and eyepiece of an astronomical telescope are double convex lenses with refractive index 1.5. When the telescope is adjusted to infinity, the separation between the two lenses is \(16 \mathrm{~cm}\). If the space between the lenses is now filled with water and again telescope is adjusted for infinity, then the present separation between the lenses isTS EAMCET 2012 Medium