Write the number in polar form with argument between 0 and 2π. −8 + 8i

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24-04-2018
Mathematics

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Write the number in polar form with argument between 0 and 2π. −8 + 8i

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CastleRook CastleRook · Answer 1 · 2018-05-04T08:02:08+02:00

CastleRook CastleRook

04-05-2018

To write from the complex to polar coordinates w proceed as follows:
Let Z=-8+8i
lZl=√(-8)²+8²=√128=8√2
Argument: θ is in second quadrant
∴ θ=π-arctan(8/8)=π-π/4=(3π)/4
∴ Z=-8+8i
=8√2[cos(3π)/4+isin(3π)/4]

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