TS EAMCET · Maths · Complex Number
Let \(z=a-\frac{i}{2} ; a \in R\). Then \(|i+z|^2-|i-z|^2\) is equal to
- A 2
- B -2
- C 4
- D -4
Answer & Solution
Correct Answer
(B) -2
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Given, } z=a-\frac{i}{2} \\ & \begin{aligned} & \therefore|i+z|^2-|i-z|^2=\left|a+\frac{i}{2}\right|^2-\left|-a+\frac{3 i}{2}\right|^2 \\ &=a^2+\left(\frac{1}{2}\right)^2-\left(a^2+\left(\frac{3}{2}\right)^2\right) \\…
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 quadratic equation whose roots are \(\sin ^2 18^{\circ}\) and \(\cos ^2 36^{\circ}\) isTS EAMCET 2023 Easy
- TS EAMCET 2019 Easy
- A binary sequence is an array of 0's and 1's. The number of \(n\)-digit binary sequences which contain even number of 0's isTS EAMCET 2009 Easy
- is a point on the conic and is a focus of that conic. is the foot of the perpendicular from on to a directrix of that conic nearer to . If , thenTS EAMCET 2021 Medium
- A line \(L\) passes through the points \(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(-2 \hat{\mathbf{i}}+3 \hat{\mathbf{k}}\). A plane \(P\) passes through the origin and the points \(4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}\). The point where the line \(L\) meets the plane \(P\) isTS EAMCET 2018 Medium
- \(L \equiv x \cos \alpha+y \sin \alpha-p=0\) represents a line perpendicular to the line \(x+y+1=0\). If \(p\) is positive, \(\alpha\) lies in the fourth quadrant and perpendicular distance from \((\sqrt{2}, \sqrt{2})\) to the line \(L=0\) is 5 units then \(p=\)TS EAMCET 2024 Medium
More PYQs from TS EAMCET
- If \(\sin \theta+\cos \theta=p\) and \(\sin ^3 \theta+\cos ^3 \theta=q\), then \(p\left(p^2-3\right)\) is equal toTS EAMCET 2013 Medium
- The following reactions is an example of ....... reaction. \(\mathrm{C}_2 \mathrm{H}_4 \mathrm{Br}_2 \longrightarrow \mathrm{C}_2 \mathrm{H}_2\)TS EAMCET 2004 Easy
- At \(27^{\circ} \mathrm{C}, 500 \mathrm{~mL}\) of helium diffuses in 30 minutes. What is the time (in hours) taken for \(1000 \mathrm{~mL}\) of \(\mathrm{SO}_2\) to diffuse under same experimental conditions?TS EAMCET 2004 Easy
- If the general solution of \(\sin x+3 \sin 3 x+\sin 5 x=0\) is \(x=y\) then the set of all values of \(\cos y\) isTS EAMCET 2018 Easy
- \(X\) litre of carbon monoxide is present at STP. It is completely oxidized to \(\mathrm{CO}_2\). The volume of \(\mathrm{CO}_2\) formed is 11.207 litres. What is the value of \(X\) in litres?TS EAMCET 2002 Easy
- The period of oscillation of a bar magnet at a place is 2 s. At the same place, the period of oscillation of another identical bar magnet whose magnetic moment is 4 times to that of first magnet isTS EAMCET 2023 Medium