Express the given complex number in the form \(a + ib: i^{9} + i^{19}\)
Solution and Explanation
\(i^{9} + i^{19}=i^{4×2+1}+i^{4×4+1}\)
\(=(i^{4})^{2} ×i +(i^{4})^{4} × i^{3}\)
\(=1×i +1×(-i)\)
\(=0\)
Top Questions on Algebra of Complex Numbers
Solve for \( x \):
\( \log_{10}(x^2) = 2 \).- BITSAT - 2025
- Mathematics
- Algebra of Complex Numbers
- Find the roots of the quadratic equation \( 2x^2 - 4x - 6 = 0 \).
- MHT CET - 2025
- Mathematics
- Algebra of Complex Numbers
- If the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \) are \( p \) and \( q \), then what is the value of \( p + q \)?
- MHT CET - 2025
- Mathematics
- Algebra of Complex Numbers
Let \( K \) be an algebraically closed field containing a finite field \( F \). Let \( L \) be the subfield of \( K \) consisting of elements of \( K \) that are algebraic over \( F \).
Consider the following statements:
S1: \( L \) is algebraically closed.
S2: \( L \) is infinite.
Then, which one of the following is correct?- GATE MA - 2025
- Mathematics
- Algebra of Complex Numbers
- If the expression \( 7 + 6x - 3x^2 \) attains its extreme value \( \beta \) at \( x = \alpha \), then the sum of the squares of the roots of the equation \( x^2 + ax - \beta = 0 \) is:
- TS EAMCET - 2024
- Mathematics
- Algebra of Complex Numbers
Questions Asked in CBSE Class XI exam
- What are the oxidation numbers of the underlined elements in each of the following and how do you rationalise your results?
(a) KI3 (b) H2S4O6 (c) Fe3O4 (d) CH3CH2OH (e) CH3COOH- CBSE Class XI
- Oxidation Number
- Using s, p, d notations, describe the orbital with the following quantum numbers.
- n=1, l=0
- n = 3, l=1
- n = 4, l =2
- n=4, l=3
- CBSE Class XI
- Developments Leading to the Bohr’s Model of Atom
- Write the following as intervals:
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}- CBSE Class XI
- Sets and their Representations
- Reduce the following equations into intercept form and find their intercepts on the axes.
(i) \(3x+2y-12=0\)
(ii) \(4x-3y=6\)
(iii) \(3y+2=0. \)- CBSE Class XI
- Distance of a Point From a Line
- If A = {-1, 1}, find A x A x A.
- CBSE Class XI
- Relations and functions
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.
