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CSCA MathematicsChapter 3: Geometry & AlgebraBeginner

Complex Numbers: Arithmetic & Modulus

复数的代数表示、四则运算与几何意义 · Node 3.3

Standard form $z = a + bi$, imaginary unit $i^2 = -1$, conjugate $\bar{z} = a - bi$, modulus $|z| = \sqrt{a^2+b^2}$, and complex plane representation.

Chapter Weight: 25% of official examination
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Core Mathematical Axiom

Formula Proof & Traps
z=a+bi,i2=−1,∣z∣=a2+b2​,c+dia+bi​=c2+d2(a+bi)(c−di)​
CSCA Exam Trap Alert

Applying $i^2 = -1$ inside a real radical or forgetting that $a, b$ must be real numbers.

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