1.13 Modulus–argument and Euler form

1.13 Modulus–argument and Euler form Quiz

IB Maths: Analysis and Approaches HL: Quiz

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  1. 1. Write 3−i\sqrt3 - \mathrm{i} in Euler form.

    • A. 2eπ6i2\mathrm{e}^{\frac{\pi}{6}\mathrm{i}}
    • B. 2e−π6i2\mathrm{e}^{-\frac{\pi}{6}\mathrm{i}}
    • C. 4e−π6i4\mathrm{e}^{-\frac{\pi}{6}\mathrm{i}}
    • D. 2e−π3i2\mathrm{e}^{-\frac{\pi}{3}\mathrm{i}}

  2. 2. Find 3eπ4i×2eπ2i3\mathrm{e}^{\frac{\pi}{4}\mathrm{i}}\times2\mathrm{e}^{\frac{\pi}{2}\mathrm{i}}.

    • A. 6eπ28i6\mathrm{e}^{\frac{\pi^2}{8}\mathrm{i}}
    • B. 5e3π4i5\mathrm{e}^{\frac{3\pi}{4}\mathrm{i}}
    • C. 6e3π4i6\mathrm{e}^{\frac{3\pi}{4}\mathrm{i}}
    • D. 6e−π4i6\mathrm{e}^{-\frac{\pi}{4}\mathrm{i}}

  3. 3. Find 8 cisπ22 cis2π3\dfrac{8\,\mathrm{cis}\frac{\pi}{2}}{2\,\mathrm{cis}\frac{2\pi}{3}}.

    • A. 4 cis(−π6)4\,\mathrm{cis}\left(-\frac{\pi}{6}\right)
    • B. 4 cis7π64\,\mathrm{cis}\frac{7\pi}{6}
    • C. 6 cis(−π6)6\,\mathrm{cis}\left(-\frac{\pi}{6}\right)
    • D. 4 cisπ64\,\mathrm{cis}\frac{\pi}{6}

  4. 4. Write 2e3π4i2\mathrm{e}^{\frac{3\pi}{4}\mathrm{i}} in Cartesian form.

    • A. 2+2 i\sqrt2 + \sqrt2\,\mathrm{i}
    • B. −2−2 i-\sqrt2 - \sqrt2\,\mathrm{i}
    • C. 2−2 i\sqrt2 - \sqrt2\,\mathrm{i}
    • D. −2+2 i-\sqrt2 + \sqrt2\,\mathrm{i}

  5. 5. The point representing zz is rotated anticlockwise by π2\frac{\pi}{2} about OO and its distance from OO is tripled. Which complex number represents the new point?

    • A. 3z+i3z + \mathrm{i}
    • B. 3iz3\mathrm{i}z
    • C. −3iz-3\mathrm{i}z
    • D. iz3\mathrm{i}z^3

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