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14 November, 08:16

Find the product of z1 and z2, where z1 = 2 (cos 70° + i sin 70°) and z2 = 4 (cos 200° + i sin 200°)

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Answers (2)
  1. 14 November, 08:34
    0
    -8i

    Step-by-step explanation:

    To multiply numbers is polar form

    z1 = r1 (cos theta 1 + i sin theta 1)

    z2 = r2 (cos theta 2 + i sin theta 2)

    z1*z2 = r1*r2 (cos (theta1+theta2) + i sin (theta1+theta2)

    z1 = 2 (cos 70° + i sin 70°)

    z2 = 4 (cos 200 + i sin 200)

    z1z2 = 2*4 (cos (70+200) + i sin (70+200)

    z1z2 = 8 (cos (270) + i sin (270))

    = 8 (0 + i (-1))

    =-8i
  2. 14 November, 10:42
    0
    Answer: - 8i

    2 (cos 70 + i sin 70) * 4 (cos 200 + isin 200)

    8 (cos (70+200) + i sin (70+200) factor a i sin 70 out

    8 (cos (270) + i sin (270))

    cos 270 is (0,-1) sin 270 is - 1 from the unit circle

    cos 270 is 0

    8 (0 - i)

    -8i
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