COMEDK · Maths · 3. Complex Number
\(\text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is }\)
- A \(49,-74\)
- B \(-47,52\)
- C \(-74,49\)
- D \(-48,-52\)
Answer & Solution
Correct Answer
(B) \(-47,52\)
Step-by-step Solution
Detailed explanation
Given the expression \((1-4i)^3 = a + ib\). Using the identity \((x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\), we substitute \(x = 1\) and \(y = 4i\). \((1-4i)^3 = (1)^3 - 3(1)^2(4i) + 3(1)(4i)^2 - (4i)^3\) \(= 1 - 12i + 3(16i^2) - 64i^3\) Since \(i^2 = -1\) and \(i^3 = -i\), we have:…
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 two circles \((x-1)^2+(y-3)^2=r^2\) and \(x^2+y^2-8 x+2 y+8=0\) intersect in two distinct points, thenCOMEDK 2022 Medium
- The function \(f(x)=\left\{\begin{array}{c}\dfrac{|x|}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.\) is discontinuous atCOMEDK 2025 Easy
- The equation of the ellipse whose centre is at the origin and the \(X\)-axis is major axis, which passes through the points \((-3,1)\) and \((2,-2)\) isCOMEDK 2014 Medium
- The total number of terms in the expansion of \((x+y)^{100}+(x-y)^{100}\) isCOMEDK 2022 Easy
- \(\text { Let } \mathrm{A} \text { and } \mathrm{B} \text { be two sets then } A-(A \cap B) \text { is equal to }\)COMEDK 2024 Easy
- Kiran purchased 3 pencils, 2 notebooks and one pen for ₹41.
From the same shop Manasa purchased 2 pencils, one notebook and 2 pens for ₹ 29, while Shreya purchased 3 pencils, 2 notebooks and 2 pens for ₹44.
The above situation can be represented in matrix form as \(A X=B\).
Then \(|\operatorname{adj} A|\) is equal toCOMEDK 2025 Medium
More PYQs from COMEDK
- What should be the value of self-inductance of an inductor that should be connected to \(220 \mathrm{~V}\) \(50 \mathrm{~Hz}\) supply, so that a maximum current of \(0.9\) A flows through it?COMEDK 2021 Medium
- A uniformly charged solid sphere of radius \(\mathrm{R}\) has potential \(\mathrm{V}_0\) (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials \(\dfrac{3 \mathrm{~V}_0}{2}, \dfrac{\mathrm{V}_0}{1}, \dfrac{3 \mathrm{~V}_0}{4}\) and \(\dfrac{\mathrm{V}_0}{4}\) have radius \(\mathrm{R}_1, \mathrm{R}_2, \mathrm{R}_3\) and \(\mathrm{R}_4\) and respectively, thenCOMEDK 2024 Hard
- If \(\lim _{x \rightarrow 1} \dfrac{x^4-1}{x-1}=\lim _{x \rightarrow k} \dfrac{x^3-k^3}{x^2-k^2}\), then the value of K isCOMEDK 2025 Easy
- The solution of the differential equation \(\dfrac{d y}{d x}+y \log y \cot x=0\) isCOMEDK 2025 Medium
- If reactance is \(\sqrt{3}\) times the resistance, then find the phase difference.COMEDK 2021 Hard
- In a nuclear reaction \({ }_4^{10} \mathrm{Be}+{ }_1^1 p \rightarrow{ }_5^{10} \mathrm{~B}+{ }_0^1 n\), what is the total energy released if the binding energy of beryllium -9 is 58.2 MeV and that of boron- 10 is 64.7 MeV ?COMEDK 2025 Medium