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Mathematics

Quadratic Equations126

Central Tendency and Dispersion 92

Linear Equations/Inequalities 91

2D-Geometry Figures 80

Polynomials 77

Exponential and Logarithmic Functions 77

Series and Sequence 73

Trigonometry 70

Permutation, Combination and Probability 69

Basic Properties of Circles 50

Equations of Circles 44

Area and Volumes 40

More About Equations 36

Variations 30

Rate, ratio and Percentage 28

Integral Indices and Rational Numbers 25

Estimation and Approximation 23

Loci 21

Coordinates 15

More About Graphs of Function 5

3D-Geometry Figures 2

Questions

Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

計算 \( i^8(4\beta i^2 + 5i - 7) \)。

2024
Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

計算 \( i^9(3\beta i^3 - 6i + 8) \)。

2024
Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

如果\(m\)是一個實數，找出表達式的實部：\[ \frac{2i}{m-2i} - \frac{3}{m+2i} \]

2024
Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

對於一個實數\(s\)，\(\frac{9i}{s+9i} + \frac{7}{s-9i}\)的實部是：

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Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

如果\(t\)是一個實數，\(\frac{10i}{t-10i} - \frac{4}{t+10i}\)的實部是：

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Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

表達式 \(2i + 3i^2 + 4i^3 + 5i^4\) 的實部是什麼？

2024
Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

\(2 + 7i + 5i^2 + 6i^3\) 的虛部是什麼？

2024
Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

計算表達式 \(\frac{3i^{17} + 4i^{18} + 5i^{19} + 6i^{20} + 7i^{21}}{1 + i}\) 的實部。

2024
Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

設 \( x = \frac{5}{b + i} \) 且 \( y = \frac{5}{b - i} \)，其中 \( b \) 為實數。下列哪些必定為真？I. \( xy \) 是一個實數。II. \( x \) 與 \( y \) 的虛部之和為 0。III. \( \frac{1}{x} \) 的實部等於 \( \frac{1}{y} \) 的實部。

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Quadratic Equations in One Unknown Perform addition, subtraction, multiplication, and division of complex numbers

設 \( p = \frac{8}{d + i} \) 且 \( q = \frac{8}{d - i} \)，其中 \( d \) 為實數。下列哪些必定為真？I. \( pq \) 是一個有理數。II. \( ip + 2 \) 與 \( iq + 2 \) 的實部相同。III. \( \frac{1}{p} \) 的實部等於 \( \frac{1}{q} \) 的實部。

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