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Concept · Geometry & Algebra
Complex arithmetic
add/subtract/multiply/divide-by-conjugate; polar form and De Moivre powers; complex numbers as rotated vectors
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Key formulas
6- z = a + bi, i2 = −1, a,b ∈ RRe(z)=a, Im(z)=b
- Modulus: |z| = √a2 + b2Conjugate: z̄ = a − bi
- Multiplication(a1+b1 i)(a2+b2 i) = (a1a2 − b1b2) + (a1b2 + a2b1)i
- Divisionmultiply numerator and denominator by the conjugate of the denominator
- Polar form: z = r(cos θ + i sin θ)De Moivre: zn = rn(cos nθ + i sin nθ)
- Rotation by ±π/2 about origin corresponds to multiplication by ±i
Shaky underneath?
If the concept underneath still feels loose, patch it here before coming back to CSCA questions.
FoundationsPrecalculus bridgeAlgebra 2 foundations