Specialist Mathematics Β· Unit 2 Β· Complex arithmetic and algebra Β· Complex arithmetic using polar form
Understand the difference between the argument, arg(π§), and the principal argument, Arg(π§) of a non-zero complex number π§. arg(π§) = Arg(π§) + 2ππ, π β β€
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Understand and use multiplication, division of complex numbers in polar form and the geometric interpretation of these. π§1 π§2 = π1 π2 cis(π1 + π2) π§1 π§2 = π 1 π 2 cis(π1 β π2)
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Use the modulus |π§| of a complex number π§ and the principal argument Arg(π§) of a non-zero complex number π§. |π§| = βπ2 + π2 Arg(π§) = π, tan(π) = π π, βπ < π β€ π, π β 0