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17 April, 16:41

Convert - √3-i to polar form.

a. 2cis (pi) / 6

b. 2cis5 (pi) / 6

c. 2cis7 (pi) / 6

d. 2cis11 (pi) / 6

e. 2cis4 (pi) / 6

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Answers (1)
  1. 17 April, 19:05
    0
    -sqrt (3) - i = 2 cis (7pi/6)

    Step-by-step explanation:

    -sqrt (3) - i

    We can find the radius

    r = sqrt ((-sqrt (3)) ^2 + (-1) ^2)

    = sqrt (3 + 1)

    = sqrt (4)

    = 2

    theta = arctan (y/x)

    arctan (-1/-sqrt (3))

    arctan (1/sqrt (3))

    theta = pi/6

    But this is in the first quadrant, and we need it in the third quadrant

    Add pi to move it to the third quadrant

    theta = pi/6 + 6pi/6

    =7pi/6

    -sqrt (3) - i = 2 cis (7pi/6)
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