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Unformatted text preview: θ so that r ≥ . Finally, polar representation of z is not unique , since e i θ = e i ( θ +2 k π ) , for any integer k ∈ Z . In other words, the pairs ( r, θ ) and ( r, θ + 2 k π ) are representations of the same z ∈ C . By convention one can restrict θ to (π , π ] or to [0 , 2 π ) and refer to it as the principal value of the argument. The principle value is usually denoted by Θ or by Arg ( z ) :π < Θ ≤ 2 π or by ≤ Θ < 2 π . We can express any argument θ in terms of its principle value Θ as θ = Θ ± 2 k π , k ∈ Z + . 1 Note that z 1 :=  z 1  ∠ z 1 and z 2 :=  z 2  ∠ z 2 ⇒ z 1 z 2 =  z 1   z 2  { ∠ z 1 + ∠ z 2 } , and z 1 z 2 =  z 1   z 2  { ∠ z 1∠ z 2 } , 1 z = 1  z  {∠ z } . This Remark is simply a pleasant visit to the Land of Complex Numbers — in your High School backyard! 2...
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 Spring '08
 Levan
 Complex number, 2k

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