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AS91577 Complex numbers

Polar and rectangular forms

AAchieved

  1. 1An Auckland electrical engineer models the impedance of part of an AC circuit as Z = −2√3 + 2i ohms: a resistance part and a reactance part. Express the impedance in polar form, r cis θ, with −π < θ ≤ π.Free
  2. 2A Christchurch electronics technician models the impedance of a filter as z = 3 − 4i ohms. Express z in polar form, r cis θ, with −π < θ ≤ π. Give θ in radians, exactly or to 3 significant figures.Free
  3. 3An Auckland wind-farm controller uses the complex gain w = 2 cis(π/3) in a phasor model. Its software only accepts numbers in the form a + bi. Convert w to rectangular form a + bi, with exact values.Free
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MMerit

  1. 21A Merit question, in the pass🔒 Pass
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EExcellence

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