COMEDK · Maths · 3. Complex Number
Evaluate \(\left[i^{22}+\left(\dfrac{1}{i}\right)^{25}\right]^3\)
- A \(4(i-1) \quad\)
- B \(2-7 i \quad\)
- C \(i-1\)
- D \(2(1-i)\)
Answer & Solution
Correct Answer
(D) \(2(1-i)\)
Step-by-step Solution
Detailed explanation
Given the expression \(\left[i^{22} + \left(\dfrac{1}{i}\right)^{25}\right]^3\). First, simplify the powers of \(i\). We know that \(i^2 = -1\), \(i^4 = 1\), and \(\dfrac{1}{i} = -i\). \(i^{22} = (i^4)^5 \times i^2 = 1^5 \times (-1) = -1\).…
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
- If tangent to the curve \(x=a t^{2}, y=2 a t\) is perpendicular to \(X\)-axis, then its point of contact isCOMEDK 2013 Easy
- If \(x, y\) and \(z\) are non-zero real numbers and \(\mathrm{a}=x \hat{i}+2 \hat{j}, \mathrm{b}=\hat{y} \hat{j}+3 \hat{k}\) and \(\mathrm{c}=x \hat{i}+y \hat{j}+z \hat{k}\) are such that \(\mathrm{a} \times \mathrm{b}=z \hat{i}-3 \hat{j}+\hat{k}\), then \([\mathrm{a b} \mathrm{c}]\) is equal toCOMEDK 2022 Hard
- If \(\sec ^{-1}\left(\frac{1+x}{1-y}\right)=a\), then \(\frac{d y}{d x}\) isCOMEDK 2020 Medium
- A five-digits number is formed by using the digits \(1,2,3,4,5\) with no repetition. The probability that the numbers 1 and 5 are always together, isCOMEDK 2023 Easy
- The curve \(x^{2}-x y+y^{2}=27\) has tangents parallel to \(X\)-axis atCOMEDK 2014 Easy
- \(\int_{-1}^{1}|1-x| d x\) is equal toCOMEDK 2013 Easy
More PYQs from COMEDK
- Zener diode is used to regulate the voltage supply because, while using a Zener diodeCOMEDK 2014 Medium
- If \(\cos A=\dfrac{3}{4}\), then \(\left(32 \sin \dfrac{A}{2} \sin \dfrac{5 A}{2}\right)=\)COMEDK 2025 Medium
- \(\alpha\)-helix and \(\beta\)-pleated structures of proteins are classified asCOMEDK 2015 Easy
- What is the maximum wave length of EM radiation required to move an electron from the valance band to conduction band of a semiconductor? [Given :Energy gap \(\mathrm{E}_{\mathrm{g}}=1.98 \times 10^{-19} \mathrm{~J}\); Planck's constant \(h=6.6 \times 10^{-34} \mathrm{Js}\) ]COMEDK 2025 Medium
- A drug that is antipyretic as well as analgesic isCOMEDK 2023 Easy
- Oil from a conical funnel is dripping at the rate of \(5 \mathrm{~cm}^3 / \mathrm{s}\). If the radius and height of the funnel are 10 cm and 20 cm respectively, then the rate at which the oil level drops when it is 5 cm from the top isCOMEDK 2025 Medium