TS EAMCET · Maths · Complex Number
If \(z=\frac{(2-i)(1+i)^3}{(1-i)^2}\), then \(\operatorname{Arg}(z)=\)
- A \(\tan ^{-1}\left(\frac{1}{3}\right)-\pi\)
- B \(\tan ^{-1}\left(\frac{3}{4}\right)-\pi\)
- C \(\pi-\tan ^{-1}\left(\frac{3}{4}\right)\)
- D \(\tan ^{-1}\left(\frac{1}{3}\right)\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1}\left(\frac{1}{3}\right)-\pi\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } z=\frac{(2-i)(1+i)^3}{(1-i)^2}=\frac{(2-i)\left(1+i^3+3 i(i+1)\right)}{\left(1+i^2-2 i\right)} \\ & =\frac{(2-i)(-2+2 i)}{-2 i}=\frac{(1-i)(2-i)}{i} \\ & =\frac{(1-i)(2 i+1)}{-1}=(-3-i)=z \quad\left(\because \text { lies in } 3^{\text {rd }} \text {…
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 period of \(\frac{\sin x}{\cos 3 x}+\frac{\sin 3 x}{\cos 9 x}+\frac{\sin 9 x}{\cos 27 x}+\frac{\sin 27 x}{\cos 81 x}\) isTS EAMCET 2020 Medium
- If \(\vec{a}=\hat{i}-\hat{j}+3 \hat{k}, \hat{c}=-\hat{k}\) are position vectors of two points and \(\vec{b}=2 \hat{i}-\hat{j}+\lambda \hat{k}, \hat{d}=\hat{i}+2 \hat{j}-\hat{k}\) are two vectors, then the lines \(\vec{r}=\vec{a}+t \vec{b}, \vec{r}=\vec{c}+s \vec{d}\) areTS EAMCET 2024 Medium
- If \(A(1,1,2), B(4,2,1)\) and \(C(2,3,5)\) are the vertices of a triangle, then a vector representing the median of the triangle through \(A\) isTS EAMCET 2020 Easy
- The differential equation corresponding to the family of curves given by \(y=a+b e^{2 x}+c e^{-3 x}\) isTS EAMCET 2018 Medium
- \(\int \frac{\log x}{(1+x)^3} d x=\)TS EAMCET 2025 Medium
- The equation of a given straight line is \(\frac{x-x_1}{\cos \theta}=\frac{y-y_1}{\sin \theta}=\gamma\). If the equation of the line perpendicular to the given line and passing through \((\alpha, \beta)\) is \(\frac{x}{a}+\frac{y}{b}=1\), then \(\frac{b}{a}\) is equal toTS EAMCET 2021 Easy
More PYQs from TS EAMCET
- The major products during the removal of temporary hardness of water areTS EAMCET 2021 Hard
- The range of the real valued function \(f(x)=|x-2|+|x-3|\) isTS EAMCET 2022 Easy
- The standard enthalpy of formation \(\left(\Delta_f H^{\circ}\right)\) of ammonia is \(-46.2 \mathrm{~kJ} \mathrm{~mol}^{-1}\). What is the \(\Delta_r H^{-}\)of the following reaction? \(\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_3(\mathrm{~g})\)TS EAMCET 2024 Easy
- The decreasing order of bond dissociation energies of \(\mathrm{C}-\mathrm{C}, \mathrm{C}-\mathrm{H}\) and \(\mathrm{H}-\mathrm{H}\) bonds isTS EAMCET 2007 Easy
- \(\lim _{x \rightarrow 0^{-}} \frac{\sqrt{\frac{1}{2}\left(1-\cos ^2 x\right)}}{x}\) is equal toTS EAMCET 2021 Easy
- If \(x+\sqrt{3} y=3\) is the tangent to the ellipse \(2 x^2+3 y^2=k\) at a point \(P\) then the equation of the normal to this ellipse at \(\mathrm{P}\) isTS EAMCET 2023 Medium