Express the given complex number in the form\( a + ib: (-2-\dfrac{1}{3}i)^3\)
Solution and Explanation
\((-2-\dfrac{1}{3}i)^3\)
\(=-[2^3+(\dfrac{i}{3})^3+3.(2)(\dfrac{i}{3})(2)(2+\dfrac{i}{3})]\)
\(=-[8+\dfrac{i^3}{27}+2i(2+\dfrac{i}{3})]\)
\(=-[8-\dfrac{i}{27}+4i-\dfrac{2}{3}]\)
\(=-[\dfrac{22}{7}+\dfrac{107}{27}i]\)
\(=-\dfrac{22}{3}-\dfrac{107}{27}i\) (Ans.)
Top Questions on Complex Numbers and Quadratic Equations
- The minimum value of \(| z+ \frac{3+4i}{2}|, |z| \leq 1\) is,
- JEE Main - 2024
- Mathematics
- Complex Numbers and Quadratic Equations
Let α,β be the roots of the equation, ax2+bx+c=0.a,b,c are real and sn=αn+βn and \(\begin{vmatrix}3 &1+s_1 &1+s_2\\1+s_1&1+s_2 &1+s_3\\1+s_2&1+s_3 &1+s_4\end{vmatrix}=\frac{k(a+b+c)^2}{a^4}\) then k=
- WBJEE - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
- For $z \in C$ if the minimum value of $(| z -3 \sqrt{2}|+| z - p \sqrt{2} i |)$ is $5 \sqrt{2}$, then a value of $p$ is ______
- JEE Main - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
- The remainder when $(11)^{1011}+(1011)^{11}$ is divided by $9$ is
- JEE Main - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
- If the shortest between the lines $\frac{x+\sqrt{6}}{2}=\frac{y-\sqrt{6}}{3}=\frac{z-\sqrt{6}}{4}$ and $\frac{x-\lambda}{3}=\frac{y-2 \sqrt{6}}{4}=\frac{z+2 \sqrt{6}}{5}$ is $6$ , then the square of sum of all possible values of $\lambda$ is
- JEE Main - 2023
- Mathematics
- Complex Numbers and Quadratic Equations
Questions Asked in CBSE Class XI exam
- Draw formulas for the first five members of each homologous series beginning with the following compounds.\((a) H–COOH (b) CH_3COCH_3 (c) H–CH=CH_2\)
- CBSE Class XI
- Organic Chemistry- Some Basic Principles and Techniques
- Distinguish between the following pairs of sentences.
(i) He was visibly moved.
(ii) He was visually impaired.- CBSE Class XI
- The adventure
- How, according to you, can peace and liberty be maintained in a state?
- CBSE Class XI
- The tale of melon City
Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- CBSE Class XI
- Pressure
- Describe the change in hybridisation (if any) of the Al atom in the following reaction.
\(AlCl_3+Cl^- \rightarrow AlCl_4^-\)- CBSE Class XI
- Hybridisation
Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
