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12 February, 21:59

Write 5 (cos109° + isin109°) in rectangular form. Round numerical entries in the answer to two decimal places.

1.63 + 4.73i

-1.63 + 4.73i

1.63 - 4.73i

-1.63 - 4.73i

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Answers (1)
  1. 12 February, 22:21
    0
    The rectangular form is - 1.63 + 4.73i ⇒ 2nd answer

    Step-by-step explanation:

    The rectangular form of r (cos Ф + i sin Ф) is x + i y, where

    x = r cos Ф y = r sin Ф

    ∵ 5 (cos 109° + i sin 109°)

    - Compare it by the form r (cos Ф + i sin Ф)

    ∴ r = 5

    ∴ Ф = 109°

    - Use the rectangular form up

    ∵ x = r cos Ф

    ∴ x = 5 cos 109°

    ∴ x = - 1.627840

    - Round it to two decimal places

    ∴ x = - 1.63

    ∵ y = r sin Ф

    ∴ y = 5 sin 109°

    ∴ y = 4.727592

    - Round it to two decimal places

    ∴ y = 4.73

    ∵ The rectangular form is x + i y

    - Substitute the values of x and y

    ∴ The rectangular form is - 1.63 + 4.73i
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