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math (please please please help)

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How to convert into polar form?

z = 1 - i

w = 1 - √3i

  • math (please please please help) -

    The polar form expresses a complex number as:

    z = |z| exp(i theta)

    theta is the angle with the positive real axis.

    For z = 1 - i, we have:

    |z| = sqrt(2)

    Then it's easy to see that you can take theta = -pi/4:

    exp(-i pi/4) = cos(pi/4) - i sin(pi/4) =
    1/sqrt(2) (1-i).

    Then in case of

    w = 1 - √3i

    you have:

    |w| = sqrt(4) = 2

    And you easly see that theta = -pi/3

    You can compute theta directly by taking arctan of imaginary part divided by the real part, but you may then need to add pi to this. If you multiply z by -1, theta changes by plus or minus pi, while the ratio stays the same.

  • math (please please please help) -

    In polar form, the first is (1/sqrt(2),-pi/4)

    The second is (2,-pi/3)

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