WBJEE · Maths · Complex Number
If \(-\pi < \arg (z) < -\frac{\pi}{2}\) then \(\arg \bar{z}-\arg (-\bar{z})\) is
- A \(\pi\)
- B \(\square \pi\)
- C \(\frac{\pi}{2}\)
- D \(-\frac{\pi}{2}\)
Answer & Solution
Correct Answer
(A) \(\pi\)
Step-by-step Solution
Detailed explanation
Hints: \[ \begin{aligned} & \text { if } \arg (z)=-\pi+\theta \\ & \Rightarrow \arg (\bar{z})=\pi-\theta \\ & \arg (-\bar{z})=-\theta \\ & \arg (\bar{z})-\arg (-\bar{z})=\pi-\theta-(-\theta)=\pi-\theta+\theta=\pi \end{aligned} \]
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 number of lines which pass through the point (2,-3) and are at a distance 8 from the point (-1,2) isWBJEE 2013 Easy
- General solution of \(y \frac{d y}{d x}+b y^{2}=a \cos x\) \(0 \leq x < 1\) is (Here, \(c\) is an arbitrary constant)WBJEE 2016 Medium
- Let \(f(x)=x^{4}-4 x^{3}+4 x^{2}+c, c \in R .\) Then,WBJEE 2019 Medium
- Let \(\mathrm{A}=\left(\begin{array}{ccc}12 & 24 & 5 \\ \mathrm{x} & 6 & 2 \\ -1 & -2 & 3\end{array}\right) .\) The value of \(\mathrm{x}\) for which the matrix \(\mathrm{A}\) is not invertible isWBJEE 2020 Easy
- Let \(f(x)\) be a differentiable function in \([2,7]\). If \(f(2)=3\) and \(f^{\prime}(x) \leq 5\) for all \(x\) in \((2,7),\) then the maximum posaible value of \(f(x)\) at \(x=7\) isWBJEE 2014 Medium
- If \(\mathrm{c}_0, \mathrm{c}_1, \mathrm{c}_2, \ldots \ldots \ldots \ldots \ldots . \mathrm{c}_{\mathrm{n}}\) denote the co-efficients in the expansion of \((1+\mathrm{x})^{\mathrm{n}}\) then the value of \(\mathrm{c}_1+2 \mathrm{c}_2+3 \mathrm{c}_3+\ldots . .+\mathrm{nc}_{\mathrm{n}}\) isWBJEE 2009 Hard
More PYQs from WBJEE
- Suppose a gaseous mixture of \(\mathrm{He}, \mathrm{Ne}, \mathrm{Ar}\) and \(\mathrm{Kr}\) is treated with photons of the frequency appropriate to ionize Ar. What ion(s) will be present in the mixture?WBJEE 2023 Easy
- Which of the following thermodynamic relation is correct?WBJEE 2010 Hard
- The polar coordinate of a point \(P\) is \(\left(2,-\frac{\pi} {4}\right)\) The polar coordinate of the point \(Q\) which is such that line joining \(P Q\) is bisected perpendicularly by the initial line, isWBJEE 2019 Medium
- In a closed circuit there is only a coil of inductance \(L\) and resistance \(100 \Omega\). The coil is situated in a uniform magnetic field. All on a sudden, the magnetic flux linked with the circuit changes by \(5 \mathrm{Weber}\). What amount of charge will flow in the circuit as a result?WBJEE 2022 Easy
- If \(\lim _{x \rightarrow 0} \frac{a x e^{x}-b \log (1+x)}{x^{2}}=3\) then the values of \(a\) and \(b\) are, respectivelyWBJEE 2015 Easy
- Acid catalysed hydrolysis of ethyl acetate follows a pseudo-first order kinetics with respect to ester. If the reaction is carried out with large excess of ester, the order with respect to ester will beWBJEE 2013 Easy