Assessment Quiz: Lesson 1: Complex Numbers in Trigonometric and Exponential Form and De Moivres Theorem

Question 1

What is the value of the algebraic expression (1 + ω - ω²)³?

Accepted Answer

-8

Answer

8

Answer

-1

Answer

1

Question 2

If $y = \sec(3x)$, then the derivative $\frac{dy}{dx}$ is equal to:

Accepted Answer

A) $3\sec(3x) 	an(3x)$

Answer

B) $\sec(3x) 	an(3x)$

Answer

C) $-3\csc(3x) \cot(3x)$

Answer

D) $3\sec^2(3x)$

Question 3

The derivative of $f(x) = 5^{x^2}$ with respect to $x$ is:

Accepted Answer

A) $2x \cdot 5^{x^2}$

Answer

B) $2x \cdot 5^{x^2} \cdot \ln 5$

Answer

C) $5^{x^2} / \ln 5$

Answer

D) $x^2 \cdot 5^{x^2 - 1}$

Question 4

If $x = \sin t$ and $y = \cos t$, then the second derivative $\frac{d^2y}{dx^2}$ is equal to:

Accepted Answer

A) $-\cos t$

Answer

B) $-\sec^3 t$

Answer

C) $-	an t$

Answer

D) $\csc^2 t$

Question 5

The slope of the normal to the curve $y = e^{2x}$ at the point where $x = 0$ is:

Accepted Answer

A) 2

Answer

B) -2

Answer

C) 1/2

Answer

D) -1/2

Question 6

The n-th term of an arithmetic sequence with first term a and common difference d is given by:

Accepted Answer

T_n = a + (n - 1) * d

Answer

T_n = a * r^(n - 1)

Answer

T_n = a + n * d

Answer

T_n = 1/2 n (2a + d)

Question 7

In the arithmetic sequence (3, 7, 11, 15, ...), the common difference d and the 20th term (T_20) are respectively:

Accepted Answer

d = 4 and T_20 = 79

Answer

d = 4 and T_20 = 83

Answer

d = 3 and T_20 = 60

Answer

d = 5 and T_20 = 98

Question 8

The sum of the first n terms of an arithmetic sequence (S_n) is formulated as:

Accepted Answer

S_n = n / 2 * [ 2a + (n - 1) * d ] = n / 2 * [ a + l ]

Answer

S_n = a * (1 - r^n) / (1 - r)

Answer

S_n = n * (a + d)

Answer

S_n = a / (1 - r)

Question 9

The common ratio r of the geometric sequence (64, 32, 16, 8, ...) is:

Accepted Answer

r = 1/2

Answer

r = 2

Answer

r = -1/2

Answer

r = 4

Question 10

The sum to infinity (S_infinity) of a geometric series exists and converges if and only if the common ratio satisfies:

Accepted Answer

|r| < 1 (i.e. -1 < r < 1), and S_infinity = a / (1 - r)

Answer

r > 1

Answer

r = 1

Answer

|r| >= 2

Point of comparison	The assimilation current	The independence current
Leader	Abbas Farhat	Messali Haj
Aim	That Algeria be part of France without Algerians enjoying rights equal to those of the French	Demanding the independence of Algeria through the "North African Star" (Étoile nord-africaine) movement

The struggle of the Algerian people after the First World War

06The struggle of the Algerian people after the First World War

Political and cultural resistance

The political currents

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