WBJEE · Maths · Complex Number

The value of \(\sum_{n=1}^{13}\left(i^{n}+i^{n+1}\right), i=\sqrt{-1}\) is

A \(i\)
B \(i-1\)
C 1
D 0

Verified Solution

Answer & Solution

Correct Answer

(B) \(i-1\)

Step-by-step Solution

Detailed explanation

We have.…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

The number of real roots of equation \(log_ex+e x=0\) is

WBJEE 2015 Easy
If \(f(x)=x^{2 / 3}, x \geq 0 .\) Then, the area of the region enclosed by the curve \(y=f(x)\) and the three lines \(y=x, x=1\) and \(x=8\) is

WBJEE 2013 Medium
The general solution of the differential equation \(\frac{d^2 y}{d x^2}+8 \frac{d y}{d x}+16 y=0\) is

WBJEE 2011 Medium
The circles \(\mathrm{x}^2+\mathrm{y}^2-10 \mathrm{x}+16=0\) and \(\mathrm{x}^2+\mathrm{y}^2=\mathrm{a}^2\) intersect at two distinct points if

WBJEE 2009 Medium
Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be given by \(f(x)=\left|x^2-1\right|\), then

WBJEE 2024 Easy
The number of onto functions from the set \(\{1,2, \ldots, 11\}\) to the set \(\{1,2, \ldots, 10\}\) is

WBJEE 2013 Easy

Explore more questions on app

From WBJEE

The value of the integral \(\int_{1}^{5}[|x-3|+|1-x|] d x\) is equal to

WBJEE 2012 Hard
The work function of Cesium is \(2.27 \mathrm{eV}\). The cut-off voltage which stops the emission of electrons from a cesium cathode irradiated with light of \(600 \mathrm{nm}\) wavelength is

WBJEE 2016 Medium
Two coherent monochromatic beams of intensities \(I\) and \(4 I\) respectively are superposed. The maximum and minimum intensitien in the reaulting pattern are

WBJEE 2014 Easy
If in case of a radio isotope the value of half-life \(\left(T_{1/2}\right)\) and decay constant \((\lambda)\) are identical in magnitude, then their value should be

WBJEE 2023 Medium
\(\mathrm{I}=\int \cos (\ln \mathrm{x}) \mathrm{dx}\). Then \(\mathrm{I}=\)

WBJEE 2022 Easy
For a plane eletromagnetic wave, the electric field is given by \(\overrightarrow{\mathrm{E}}=90 \sin \left(0.5 \times 10^{3} \mathrm{x}+1.5 \times 10^{11} \mathrm{t}\right) \mathrm{k} . \mathrm{v} / \mathrm{m} .\) The corresponding magnetic field \(\vec{B}\) will be

WBJEE 2021 Easy

Explore more questions on app