KCET · Maths · Complex Number
If \( \left(\frac{1-i}{1+i}\right)^{96}=a+i b \) then \( (a, b) \) is
- A \( (1,1) \)
- B \( (1,0) \)
- C \( (0,1) \)
- D \( (0,-1) \)
Answer & Solution
Correct Answer
(B) \( (1,0) \)
Step-by-step Solution
Detailed explanation
Given that,
\( \left(\frac{1-i}{1+i}\right)^{96}=a+i b \)
Now, \( \frac{1-i}{1+i}=\frac{1-i}{1+i} \times \frac{1-i}{1-i}=-i \)
So, \( i^{96}=a+i b \)
\( \Rightarrow\left(i^{4}\right)^{24}=a+i b \)
\( \Rightarrow 1+i(0)=a+i b \)
Therefore, \( (a, b) \) is \( (1,0) \).
\( \left(\frac{1-i}{1+i}\right)^{96}=a+i b \)
Now, \( \frac{1-i}{1+i}=\frac{1-i}{1+i} \times \frac{1-i}{1-i}=-i \)
So, \( i^{96}=a+i b \)
\( \Rightarrow\left(i^{4}\right)^{24}=a+i b \)
\( \Rightarrow 1+i(0)=a+i b \)
Therefore, \( (a, b) \) is \( (1,0) \).
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 \( \cos \alpha, \cos \beta, \cos \gamma \) are the direction cosines of a vector \( \vec{a} \), then \( \cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma \) is
equal toKCET 2016 Medium - The value of \(\int_{0}^{4}|x-1| d x\) isKCET 2011 Easy
- A straight line passes through the points \( (5,0) \) and \( (0,3) \). The length of perpendicular from the
point \( (4,4) \) on the line isKCET 2014 Easy - \( X Y \) - plane divides the line joining the points \( A(2,3,-5) \) and \( B(-1,-2,-3) \) in the ratioKCET 2019 Easy
- The smallest positive divisor greater than 1 of a composite number \(a\) isKCET 2013 Medium
- Let \(R\) be an equivalence relation defined on a set containing 6 elements. The minimum number or ordered pairs that \(R\) should contain isKCET 2010 Easy
More PYQs from KCET
- Equation of line passing through the point \( (1,2) \) and perpendicular to the line
\( y=3 x-1 \)KCET 2017 Medium - Increasing order of carbon-carbon bond length for the following is
KCET 2011 Easy - In nephron, transport of substances like sodium chloride and urea is facilitated by the special arrangement called counter current mechanism that comprises ofKCET 2025 Medium
- If ' \( X \) ' has a binomial distribution with parameters \( n=6, p \) and \( P(X=2)=12, P(X=3)=5 \) then
\( P= \)KCET 2019 Easy - A solution of two liquids boils at a temperature more than the boiling point of either of them. Hence, the binary solution showsKCET 2011 Easy
- The two lines \(l x+m y=n\) and \(l^{\prime} x+m^{\prime} y=n^{\prime}\) are perpendicular ifKCET 2020 Easy