Page 796 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

But these are just Formulas 3 and 5 in a different notation.
We conclude this section with a useful formula for in polar notation. If

then

Recalling the trigonometric identities (13)
we can rewrite 13 as
or, equivalently, (14)
(15)
In the special case where , the polar form of z is , and 14 yields the formula

Exercise Set 10.3

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In each part, find the principal argument of z.
1.

(a)
(b)
(c)
(d)
(e)
(f)