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10.5E: Fomu ya Polar ya Hesabu Complex (Mazoezi)

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    Kwa mazoezi yafuatayo, pata thamani kamili ya kila nambari tata.

    28. \(-2+6 \mathbf{i}\)

    29. \(4-3 \mathbf{i}\)

    Andika namba tata katika fomu ya polar.

    30. \(5+9 \mathbf{i}\)

    31. \(\frac{1}{2}-\frac{\sqrt{3}}{2} \mathbf{i}\)

    Kwa mazoezi yafuatayo, kubadilisha namba tata kutoka polar hadi fomu ya mstatili.

    32. \(z=5 \operatorname{cis}\left(\frac{5 \pi}{6}\right)\)

    33. \(z=3 \operatorname{cis}\left(40^{\circ}\right)\)

    Kwa mazoezi yafuatayo, pata bidhaa\(z_{1} z_{2}\) katika fomu ya polar.

    34.

    \(z_{1}=2 \operatorname{cis}\left(89^{\circ}\right)\)

    \(z_{2}=5 \operatorname{cis}\left(23^{\circ}\right)\)

    35.

    \(z_{1}=10\)cis\(\left(\frac{\pi}{6}\right)\)

    \(z_{2}=6 \operatorname{cis}\left(\frac{\pi}{3}\right)\)

    Kwa mazoezi yafuatayo, pata quotient\(\frac{z_{1}}{z_{2}}\) katika fomu ya polar.

    36. \(z_{1}=12 \operatorname{cis}\left(55^{\circ}\right)\)

    \(z_{2}=3 \operatorname{cis}\left(18^{\circ}\right)\)

    37. \(z_{1}=27 \operatorname{cis}\left(\frac{5 \pi}{3}\right)\)

    \(z_{2}=9 \operatorname{cis}\left(\frac{\pi}{3}\right)\)

    Kwa mazoezi yafuatayo, pata nguvu za kila nambari tata katika fomu ya polar.

    38. Kupata\(z^{4}\) wakati\(z=2\) cis\(\left(70^{\circ}\right)\)

    39. Kupata\(z^{2}\) wakati\(z=5\) cis\(\left(\frac{3 \pi}{4}\right)\)

    Kwa mazoezi yafuatayo, tathmini kila mizizi.

    40. Tathmini mizizi ya mchemraba wa\(z\) wakati\(z=64\) cis\(\left(210^{\circ}\right)\).

    41. Tathmini mizizi ya mraba ya\(z\) wakati\(z=25\) cis\(\left(\frac{3 \pi}{2}\right)\).

    Kwa mazoezi yafuatayo, njama namba tata katika ndege tata.

    42. \(6-2 \mathbf{i}\)

    43. \(-1+3 \mathbf{i}\)