JEE Mains · Maths · STD 11 - 4.1 complex nubers
If the four complex numbers \(z\), \(\overline{ z }, \overline{ z }-2 \operatorname{Re}(\overline{ z })\) and \(z -2 \operatorname{Re}( z )\) represent the vertices of a square of side \(4\) units in the Argand plane, then \(|z|\) is equal to
- A \(4\)
- B \(2\)
- C \(4 \sqrt{2}\)
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Let \(z=x+i y\) Length of side \(=4\) \(A B=4\) \(|z-\bar{z}|=4\) \(|2 y|=4 ;|y|=2\) \(B C=4\) \(\mid \overline{ z }-(\overline{ z }-2 \operatorname{Re}(\overline{ z }) \mid=4\) \(|2 x|=4 ;|x|=2\) \(|z|=\sqrt{x^{2}+y^{2}}=\sqrt{4+4}=2 \sqrt{2}\)
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
- Suppose a class has \(7\) students. The average marks of these students in the mathematics examination is \(62\), and their variance is \(20\) . A student fails in the examination if \(he/she\) gets less than \(50\) marks, then in worst case, the number of students can fail isJEE Mains 2022 Medium
- Let \(A\) and \(B\) be \(3 \times 3\) real matrices such that \(A\) is symmetric matrix and \(B\) is skew-symmetric matrix. Then the system of linear equations \(\left( A ^{2} B ^{2}- B ^{2} A ^{2}\right) X = O ,\) where \(X\) is a \(3 \times 1\) column matrix of unknown variables and \(O\) is a \(3 \times 1\) null matrix, has ....... .JEE Mains 2021 Hard
- Let \(X\) be a random variable such that the probability function of a distribution is given by \(P(X=\) 0) \(=\frac{1}{2}, \mathrm{P}(\mathrm{X}=\mathrm{j})=\frac{1}{3^{j}}(\mathrm{j}=1,2,3, \ldots, \infty)\). Then the mean of the distribution and \(\mathrm{P}(\mathrm{X}\) is positive and even) respectively are:JEE Mains 2021 Medium
- \(\lim _{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2} \sin 2 x}\) is equal toJEE Mains 2022 Hard
- For three events \(A,B \) and \(C\) ,\(P (\) Exactly one of \(A\) or \(B\) occurs\()\, =\, P (\) Exactly one of \(C\) or \(A\) occurs \() =\) \(\frac{1}{4}\) and \(P (\) All the three events occur simultaneously \() =\) \(\frac{1}{16}\) Then the probability that at least one of the events occurs is :JEE Mains 2017 Hard
- Let \(\alpha, \beta(\alpha \neq \beta)\) be the values of m , for which the equations \(x+y+z=1 ; x+2 y+4 z=\mathrm{m}\) and \(x+4 y+10 z=m^2\) have infinitely many solutions. Then the value of \(\sum_{n=1}^{10}\left(n^\alpha+n^\beta\right)\) is equal to :JEE Mains 2025 Easy
More PYQs from JEE Mains
- Let \(\mathrm{f}(\mathrm{x})\) be a polynomial of degree \(3\) such that \(\mathrm{f}(\mathrm{k})=-\frac{2}{\mathrm{k}}\) for \(\mathrm{k}=2,3,4,5 .\) Then the value of \(52-10 \mathrm{f}(10)\) is equal to :JEE Mains 2021 Hard
- A bag contains \(6\) balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least \(5\) black balls isJEE Mains 2023 Hard
- The value of \({\int\limits_0^x {\left| {\cos \,x} \right|} ^3}\,dx\) isJEE Mains 2019 Hard
- If the area of the region \(\left\{(x, y):-1 \leq x \leq 1,0 \leq y \leq a+\mathrm{e}^{|x|}-\mathrm{e}^{-x}, \mathrm{a}\gt0\right\}\) is \(\frac{\mathrm{e}^2+8 \mathrm{e}+1}{\mathrm{e}}\), then the value of \(a\) is :JEE Mains 2025 Medium
- If the number of integral terms in the expansion of \(\left(3^{\frac{1}{2}}+5^{\frac{1}{8}}\right)^{\text {n }}\) is exactly \(33,\) then the least value of \(n\) isJEE Mains 2020 Medium
- Let a be an integer such that \(\lim \limits_{x \rightarrow 7} \frac{18-[1-x]}{[x-3 a]}\) exists, where \([ t ]\) is greatest integer \(\leq t\). Then a is equal toJEE Mains 2022 Hard