AP EAMCET · Maths · Complex Number
If \(z=3+5 i\), then \(z^3+\bar{z}+198\) is equal to
- A \(-3-5 i\)
- B \(-3+5 i\)
- C \(3-5 i\)
- D \(3+5 i\)
Answer & Solution
Correct Answer
(D) \(3+5 i\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} z & =3+5 i \\ \therefore \quad \bar{z} & =3-5 i \\ z^3 & =z^2 \cdot z=(3+5 i)^2(3+5 i) \\ & =(9-25+30 i)(3+5 i) \\ & =(-16+30 i)(3+5 i) \\ & =-48-150+10 i \\ & =-198+10 i \end{aligned} \] Now,…
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
- Let \(\mathbf{u}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}\) and \(\mathbf{v}=-3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}\). Consider three points \(P, Q\) and \(R\) having position vectors \(\frac{-1}{7} \hat{\mathbf{i}}, \frac{-1}{4} \hat{\mathbf{j}}\) and \(-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}\) respectively.
Among these, the points in the line segment passing through \(\mathbf{u}\) and \(\mathbf{v}\) areAP EAMCET 2020 Easy - By the definition of the definite integral, the value of
\[
\lim _{n \rightarrow \infty}\left(\frac{1}{\sqrt{n^2-1}}+\frac{1}{\sqrt{n^2-2^2}}+\ldots+\frac{1}{\sqrt{n^2-(n-1)^2}}\right)
\]
is equal toAP EAMCET 2016 Easy - If \(f(x)=|x|+|\sin x|\) for \(x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\), then its left hand derivative at \(x=0\) isAP EAMCET 2011 Easy
- If \(p(x)\) is a polynomial of degree 3 which satisfies \(p^{\prime \prime}(1)=0\) and \(p^{\prime \prime \prime}(1)=6\), then \(p^{\prime \prime}(0)\) is equal toAP EAMCET 2021 Medium
- The system of equations \(3 x+2 y+z=6\), \(3 x+4 y+3 z=14\) and \(6 x+10 y+8 z=a\), has infinite number of solutions, if \(a\) is equal toAP EAMCET 2013 Hard
- The equation of the circle whose diameter is the common chord of the circles \(x^2+y^2+2 x+2 y+1=0\) and \(x^2+y^2+4 x+6 y+4=0\) isAP EAMCET 2017 Hard
More PYQs from AP EAMCET
- A Grignard reagent \((\mathrm{X})\) on reaction with carbonyl compound \((\mathrm{Y})\) followed by hydrolysis gave Z . Z reacts with cone. HCl at room temperature. X and Y respectively areAP EAMCET 2024 Hard
- If the equations \(\mathrm{x}=\mathrm{t}^2+\mathrm{t}+1, \mathrm{y}=\mathrm{t}^2-\mathrm{t}+1\) represents a curve \(\mathrm{C}\) with parameter \(\mathrm{t}\), then the Cartesian equation of \(\mathrm{C}\) isAP EAMCET 2023 Easy
- Acid hydrolysis of \(X\) yields two different organic compounds. Which one of the following is \(X\) ?AP EAMCET 2003 Easy
- \(\triangle \mathrm{ABC}\) is formed by \(\mathrm{A}(1,8,4), \mathrm{B}(0,-11,4)\) and \(C(2,-3,1)\). If \(D\) is the foot of the perpendicular drawn from \(\mathrm{A}\) to \(\mathrm{BC}\), then the coordinates of \(\mathrm{D}\) areAP EAMCET 2023 Easy
- General solution of \(4 \sin ^2(x)-4 \sin (x)+1=0\) isAP EAMCET 2020 Easy
- A pair of lines \(S=\mathbf{0}\) together with the lines given by the equation \(8 x^2-14 x y+3 y^2+10 x+10 y-25=0\) form a parallelogram. If its diagonals intersect at the point \((3,2)\), then the equation \(S=0\), isAP EAMCET 2019 Medium