Q. If Y is the sister of Z and A is the mother of Z, how is Y related to A? (2023)
-
A.
Daughter
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B.
Sister
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C.
Niece
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D.
Cousin
Solution
Y is the sister of Z, making her A's daughter as well.
Correct Answer: B — Sister
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Q. If you add 12.11 and 0.3, how many decimal places should the answer have?
Solution
The answer should have 1 decimal place, as 0.3 has the least decimal places.
Correct Answer: A — 1
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Q. If you are facing North and turn 90 degrees to your right, which direction are you facing? (2020)
-
A.
East
-
B.
West
-
C.
South
-
D.
North-East
Solution
Turning 90 degrees to the right from North will direct you to East.
Correct Answer: A — East
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Q. If you are moving South and want to go East, which way should you turn? (2021)
-
A.
Left
-
B.
Right
-
C.
Backwards
-
D.
No turn needed
Solution
To go from South to East, you need to turn right.
Correct Answer: B — Right
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Q. If you have 0.25 moles of sulfuric acid (H2SO4), what is its mass? (2023)
-
A.
49 g
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B.
98 g
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C.
25 g
-
D.
12.5 g
Solution
Molar mass of H2SO4 = 2*1 + 32 + 4*16 = 98 g/mol. Mass = 0.25 moles x 98 g/mol = 24.5 g.
Correct Answer: B — 98 g
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Q. If you multiply 2.5 (2 significant figures) by 3.42 (3 significant figures), how many significant figures should the answer have?
Solution
The answer should have 2 significant figures, as the least number of significant figures in the factors is 2.
Correct Answer: A — 2
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Q. If you multiply 2.5 (2 significant figures) by 3.42 (3 significant figures), how many significant figures should the result have?
Solution
The result should have 2 significant figures, as the least number of significant figures in the factors is 2.
Correct Answer: A — 2
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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 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 = 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 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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