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Complex Numbers, EXT2 N1 EQ-Bank 5 MC

In which quadrant of the complex plane is the complex number  \(4e^{\small{\dfrac{i16}{3}}}\)  found?

  1. I
  2. II
  3. III
  4. IV
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\(\D\)

Show Worked Solution

\(z=4 e^{\small{\dfrac{in6}{3}}}\)

\(\arg (z)=\dfrac{16}{3} \approx 5.3\)

\(\dfrac{3 \pi}{2}<5.3<2 \pi\)

\(\therefore \ \text{Quadrant IV}\)

\(\Rightarrow D\)

Filed Under: Exponential Form Tagged With: Band 3, smc-1191-10-Argand diagrams

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