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

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William Bean

Mathematics

11 September, 19:11

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

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Eden Donaldson · Answer 1

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]