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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