Q. If you were to predict future sales based on the table, which product would you recommend investing in?
-
A.
Product A
-
B.
Product B
-
C.
Product C
-
D.
Product D
Solution
Investing in Product A is recommended due to its consistent growth trend.
Correct Answer:
A
— Product A
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Q. If you were to predict the sales for Product B in Q5 based on the table, what would be a reasonable estimate?
-
A.
600 units
-
B.
650 units
-
C.
700 units
-
D.
750 units
Solution
Based on the growth trend, a reasonable estimate for Product B's sales in Q5 would be 700 units.
Correct Answer:
C
— 700 units
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Q. If you were to rank the products based on their average sales per quarter, which product would rank the highest?
-
A.
Product A
-
B.
Product B
-
C.
Product C
-
D.
Product D
Solution
Product B ranks the highest based on its average sales per quarter.
Correct Answer:
B
— Product B
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Q. If you were to rank the products based on their Q4 sales, which would be last?
-
A.
Product A
-
B.
Product B
-
C.
Product C
-
D.
Product D
Solution
Product D would be last based on its Q4 sales figures.
Correct Answer:
D
— Product D
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Q. If you were to summarize the overall performance of Product D, which option would be most accurate?
-
A.
Consistent growth
-
B.
Fluctuating sales
-
C.
Declining popularity
-
D.
Stable performance
Solution
Product D shows fluctuating sales across the quarters as per the table.
Correct Answer:
B
— Fluctuating sales
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Q. If z = -1 + i, what is the square of the modulus of z?
Solution
The modulus of z = -1 + i is |z| = √((-1)² + 1²) = √(1 + 1) = √2. The square of the modulus is |z|² = 2.
Correct Answer:
D
— 5
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Q. If z = -2 + 2i, what is the value of |z|? (2019)
Solution
|z| = √((-2)^2 + (2)^2) = √(4 + 4) = √8 = 2√2.
Correct Answer:
A
— 2√2
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Q. If z = -3 + 4i, what is the real part of z?
Solution
The real part of a complex number z = a + bi is a. Here, the real part is -3.
Correct Answer:
A
— -3
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Q. If z = 1 + i, find the conjugate of z.
-
A.
1 - i
-
B.
1 + i
-
C.
-1 + i
-
D.
-1 - i
Solution
The conjugate of z = 1 + i is z̅ = 1 - i.
Correct Answer:
A
— 1 - i
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Q. If z = 1 + i, find the value of z^3.
-
A.
-2 + 2i
-
B.
2 + 2i
-
C.
0
-
D.
1 + 3i
Solution
z^3 = (1 + i)^3 = 1 + 3i - 3 - i = -2 + 2i.
Correct Answer:
A
— -2 + 2i
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Q. If z = 1 + i, find the value of z^4.
Solution
z^4 = (1 + i)^4 = (2e^(iπ/4))^4 = 16e^(iπ) = -16.
Correct Answer:
A
— -4
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Q. If z = 1 + i, find z^2.
-
A.
2i
-
B.
2
-
C.
1 + 2i
-
D.
0
Solution
z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Correct Answer:
C
— 1 + 2i
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Q. If z = 1 + i, find z^3.
-
A.
-2 + 2i
-
B.
2 + 2i
-
C.
0
-
D.
1 + i
Solution
z^3 = (1 + i)^3 = 1 + 3i - 3 - i = -2 + 2i.
Correct Answer:
A
— -2 + 2i
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Q. If z = 1 + i, find z^4.
Solution
z^4 = (1 + i)^4 = 4i.
Correct Answer:
A
— -4
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Q. If z = 1 + i, find |z|².
Solution
|z|² = (1)² + (1)² = 1 + 1 = 2.
Correct Answer:
B
— 2
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Q. If z = 1 + i, what is the argument of z?
Solution
The argument of a complex number z = a + bi is given by θ = tan⁻¹(b/a). Here, θ = tan⁻¹(1/1) = π/4.
Correct Answer:
A
— π/4
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Q. If z = 1 + i, what is the value of z^2? (2022)
-
A.
2i
-
B.
1 + 2i
-
C.
2
-
D.
0
Solution
z^2 = (1 + i)^2 = 1^2 + 2(1)(i) + i^2 = 1 + 2i - 1 = 2i.
Correct Answer:
B
— 1 + 2i
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Q. If z = 1 + i, what is the value of z^3? (2023)
-
A.
-2 + 2i
-
B.
2i
-
C.
0
-
D.
2 + 2i
Solution
z^3 = (1 + i)^3 = 1 + 3i + 3i^2 + i^3 = 1 + 3i - 3 - i = -2 + 2i.
Correct Answer:
A
— -2 + 2i
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Q. If z = 1 + i, what is the value of z²? (2022)
-
A.
0
-
B.
2i
-
C.
2
-
D.
1 + 2i
Solution
z² = (1 + i)² = 1² + 2(1)(i) + i² = 1 + 2i - 1 = 2i.
Correct Answer:
D
— 1 + 2i
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Q. If z = 1 + i, what is z^2?
-
A.
2i
-
B.
2
-
C.
1 + 2i
-
D.
0
Solution
z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i.
Correct Answer:
C
— 1 + 2i
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Q. If z = 1 + i√3, find the argument of z.
-
A.
π/3
-
B.
2π/3
-
C.
π/6
-
D.
5π/6
Solution
The argument θ = tan^(-1)(√3/1) = π/3.
Correct Answer:
A
— π/3
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Q. If z = 1 + i√3, find the conjugate of z.
-
A.
1 - i√3
-
B.
1 + i√3
-
C.
1 + √3i
-
D.
1 - √3i
Solution
The conjugate of a complex number z = a + bi is given by z* = a - bi. Thus, the conjugate of z = 1 + i√3 is 1 - i√3.
Correct Answer:
A
— 1 - i√3
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Q. If z = 1 + i√3, find the modulus of z.
Solution
|z| = √(1^2 + (√3)^2) = √(1 + 3) = √4 = 2.
Correct Answer:
A
— 2
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Q. If z = 1 + i√3, find the value of |z|^2.
Solution
|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
Correct Answer:
A
— 4
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Q. If z = 1 + i√3, find |z|.
Solution
|z| = √(1^2 + (√3)^2) = √(1 + 3) = √4 = 2.
Correct Answer:
A
— 2
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Q. If z = 1 + i√3, find |z|^2.
Solution
|z|^2 = (1)^2 + (√3)^2 = 1 + 3 = 4.
Correct Answer:
A
— 4
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Q. If z = 1 + i√3, then the argument of z is?
-
A.
π/3
-
B.
π/6
-
C.
2π/3
-
D.
5π/6
Solution
The argument θ = tan^(-1)(√3/1) = π/3.
Correct Answer:
A
— π/3
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Q. If z = 1 + i√3, what is the value of z^2? (2023)
-
A.
-2 + 2i√3
-
B.
4
-
C.
1 - 2i√3
-
D.
1 + 2i√3
Solution
z^2 = (1 + i√3)^2 = 1^2 + 2(1)(i√3) + (i√3)^2 = 1 + 2i√3 - 3 = -2 + 2i√3.
Correct Answer:
A
— -2 + 2i√3
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Q. If z = 1 + i√3, what is |z|^2?
Solution
|z|^2 = 1^2 + (√3)^2 = 1 + 3 = 4.
Correct Answer:
A
— 4
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Q. If z = 1 + √3i, what is the argument of z? (2015)
-
A.
π/3
-
B.
π/6
-
C.
2π/3
-
D.
3π/4
Solution
The argument is given by tan^(-1)(√3/1) = π/3.
Correct Answer:
A
— π/3
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