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12 November, 01:21

Write the complex number - 2+2i in polar form

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  1. 12 November, 03:22
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    For polar form you need to find the modulus (length of the vector) and the argument (angle of the vector) and present in form rcis (Arg) or re^Argi

    start with the modulus r=sqrt (a^2 + b^2)

    =sqrt (-2^2 + 2^2)

    = sqrt (4+4)

    =sqrt (8)

    =2sqrt (2)

    next the argument, firstly arg=tan (b/a)

    = tan (2/2)

    =tan (1)

    =pi/4. (exact values table)

    Now consider the quadrant the complex number is in, as it is (-2,2) it is in the second quadrant and as such your Arg value is:

    Arg=pi-arg

    = pi-pi/4

    = 3pi/4

    add it all together and your complex number in polar form is:

    2sqrt2cis (3pi/4)

    note: cis is short hand for cos (x) + isin (x), it is possible your tutor would rather you use the complex exponential form which is simply re^Argi and your answer would look like:

    2sqrt2e^ (3pi/4) i

    Also notice the difference between arg and Arg as this often slips students up and always present Arg in prinicple argument form ie - pi
    Hopefully this has been clear enough and good luck
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