Podcast
Questions and Answers
What is the result of the expression $\frac{1+i}{1-i}$?
What is the result of the expression $\frac{1+i}{1-i}$?
- 2
- 1
- -i
- i (correct)
When expressing $\frac{2-5i}{1-4i}$ in the form of $a + ib$, what is the value of $a$?
When expressing $\frac{2-5i}{1-4i}$ in the form of $a + ib$, what is the value of $a$?
- 2
- 0 (correct)
- -1
- 1
What is the constant term in the expansion of $(2x + 3x^2)^5$?
What is the constant term in the expansion of $(2x + 3x^2)^5$?
- 81 (correct)
- 0
- 75
- 243
If $C_r = C_{r+2}$, what can be inferred about the value of $C_4$?
If $C_r = C_{r+2}$, what can be inferred about the value of $C_4$?
In the expression $P_n = \frac{n!}{r!(n-r)!}$, when $P_6 = 20 \times P_4$, what is the value of $n$?
In the expression $P_n = \frac{n!}{r!(n-r)!}$, when $P_6 = 20 \times P_4$, what is the value of $n$?
Flashcards
Complex Number
Complex Number
A number in the form a + bi, where a and b are real numbers and i is the imaginary unit (i² = -1).
Partial Fraction Decomposition
Partial Fraction Decomposition
A technique to break down a complex fraction into simpler fractions.
Binomial Expansion
Binomial Expansion
A method for expanding expressions in the form (x + y)^n.
Permutations
Permutations
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Combinations
Combinations
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Study Notes
Question 1
- Prove that (1+i)n = in
Question 2
- Express (2-5i)/(1-4i) into the form of a+ib
Question 3
- Resolve into partial fractions:
- (a) (2x-1)/((x-1)(2x+3))
- (b) (9x+11)/((x-1)(x2+3x+1))
- (c) (x2+2)/((x-1)(x-2)2)
- (d) (x2+x)/((x-1)2(x2+4))
Question 4
- Find the constant term in the expansion of (2x+3x-3)9
Question 5
- Find the middle term in the expansion of (2x2-1/x)7
Question 6
- Find the value of n, when nP6 = 20 × nP4
Question 7
- If 18Cr = 18Cr+2 then find the value of Cr
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Description
Test your understanding of complex numbers and polynomial expansions with this Algebra Class 10 Quiz. The quiz includes problems on proving identities, partial fractions, binomial expansion, and combinations. Challenge yourself and see how well you can navigate these concepts!
