Show that every complex number z = x+iy can be written in the form z =...

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Show that every complex number z = x+iy can be written in the form z = reio, where r is unique and in the range 0 ≤r <∞, and 0 € R is unique up to an integer multiple of 27. Check that r = |z| and 0 = arctan(y/x) Ө whenever these formulas make sense. Show that every complex number z = x+iy can be written in the form z = reio, where r is unique and in the range 0 ≤r <∞, and 0 € R is unique up to an integer multiple of 27. Check that r = |z| and 0 = arctan(y/x) Ө whenever these formulas make sense.

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z xiyre rcos 0 i sin 0 So thatr cos 0 ir sin r And as 20r0 We must ... View the full answer