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4 November, 03:05

Write each complex number in rectangular form.

a. 2 (cos (135) + i sin (135))

b. 3 (cos (120)) + i sin (120))

c. 5 (cos (5pi/4) + i sin (5pi/4))

d. 4 (cos (5pi/3) + i sin (5pi/3))

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Answers (1)
  1. 4 November, 03:07
    0
    Hello,

    A)

    cos 135° = - cos 45°=-√2/2

    sin 135°=sin45°=√2/2

    2 (cos 135°+i sin 135°) = - √2 + i*√2

    B)

    cos 120°=-cos 30°=-√3 / 2

    sin 120°=sin 30°=1/2

    3 (cos 120° + i sin 120) = - 3/2*√3 + i*3/2

    C)

    cos (5π/4) = - cos (π/4) = - √2 / 2

    sin (5π/4) = - sin (π/4) = - √2 / 2

    5 (cos (5π/4) + i sin (5π/4)) = - 5/2*√2 + i * 5/2*√2

    D)

    cos (5π/3) = cos (π/3) = √3 / 2

    sin (5π/3) = - sin (π/3) = - 1/2

    4 (cos (5pi/3) + i sin (5pi/3))

    =2√3 - 2*i
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