Question

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

Answer 1

Answer:

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