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ac7597
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Summary:: Hello, my question asks if the complex exponential equation 4e^(-j) is equal to 4 ∠-180°. I tried to use polar/rectangular conversions: a+bj=c∠θ with c=(√a^2 +b^2) and θ=tan^(-1)[b/a]
4e^(-j)=4 ∠-180°
c=4, 4=(√a^2 +b^2)
solving for a : a=(√16-b^2)
θ=tan^(-1)[b/a]= -1
b/(√16-b^2)= tan(-1)
b=(√16-b^2)* tan(-1)
b=(√16-b^2)* -1.557
b^2=(16-b^2)(-1.557)^2
solving for b: b=3.365
4=(√a^2 +3.365^2) thus a=2.161
θ=tan^(-1)[-3.365/2.161]= -57.3°
Thus it is false
[Moderator's note: Moved from a technical forum and thus no template.]
4e^(-j)=4 ∠-180°
c=4, 4=(√a^2 +b^2)
solving for a : a=(√16-b^2)
θ=tan^(-1)[b/a]= -1
b/(√16-b^2)= tan(-1)
b=(√16-b^2)* tan(-1)
b=(√16-b^2)* -1.557
b^2=(16-b^2)(-1.557)^2
solving for b: b=3.365
4=(√a^2 +3.365^2) thus a=2.161
θ=tan^(-1)[-3.365/2.161]= -57.3°
Thus it is false
[Moderator's note: Moved from a technical forum and thus no template.]
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