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Mathematics
Averi Barajas
12 November, 01:21
Write the complex number - 2+2i in polar form
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Morgan Valenzuela
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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