COMEDK · Maths · 3. Complex Number

If \((1+i)^{200}=2^{98}(a+i b)\) then the value of \(a+b\) is

Verified Solution

Answer & Solution

Correct Answer

(B) 4

Step-by-step Solution

Detailed explanation

We have, \((1+i)^{200}\) Multiply and divide by \(\sqrt{2}\)…

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 mean and variance for the data \(6,7,10,12\), \(13,4,8,12\) respectively are

COMEDK 2015 Medium
The slope of lines which makes an angle \(60^{\circ}\) with the line \(y-3 x+18=0\)

COMEDK 2023 Medium
If for real values of \(x, \cos \theta=x+\dfrac{1}{x}\), then

COMEDK 2025 Medium
If \(f(x)\) is a function such that \(f^{\prime \prime}(x)+f(x)=0\) and \(g(x)=[f(x)]^{2}+\left[f^{\prime}(x)\right]^{2}\) and \(g(3)+8\), then \(g(8)=\)

COMEDK 2016 Easy
A ladders \(5 \mathrm{~m}\) long is leaning against a wall. The bottom of the ladder is pulled along the ground away from the wall, at the rate of \(2 \mathrm{~m} / \mathrm{sec}\). The speed at which its height on the wall decreases when the foot of the ladder is \(4 \mathrm{~m}\) away from the wall is

COMEDK 2015 Easy
\(\int \left(\sin^6 x + \cos^6 x + 3\sin^2 x \cos^2 x\right)\, dx =\)

COMEDK 2026 Easy

Explore more questions on app

From COMEDK

Bromo ethane and isopropyl chloride with metallic sodium in ether forms

COMEDK 2019 Easy
Choose the incorrect statement from the following.

COMEDK 2025 Medium
Chords of the circle \(x^{2}+y^{2}=r^{2}\) touch the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\). The locus of the mid-points of the chords is

COMEDK 2017 Hard
In a meter bridge a copper coil is connected in the right gap and a resistance of \(10 \Omega\) in the left gap. The balance point is obtained at \(0.2 \mathrm{~m}\). The resistance of the coil is

COMEDK 2012 Medium
Bohr's radius of \(2 \mathrm{nd}\) orbit of \(\mathrm{Be}^{3+}\) is equal to that of

COMEDK 2023 Easy
The sides of a parallelogram are represented by vectors \(\mathbf{p}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{q}=3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) Then, the area of the parallelogram is

COMEDK 2023 Easy

Explore more questions on app