How do you write the complex number in trigonometric form $- 3 - i$ $-3-i$ ?

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Answer 1 · 2018-01-06T01:08:42

$\sqrt{10} \cdot C i s (π + arctan (\frac{1}{3}))$ $sqrt10*Cis(pi+arctan(1/3))$

Magnitute of z=-3-i; $r = \sqrt{{(- 3)}^{2} + {(- 1)}^{2}} = \sqrt{10}$ $r=sqrt((-3)^2+(-1)^2)=sqrt10$

Argument of z; $A r g (z) = arctan (\frac{- 1}{- 3}) = arctan (\frac{1}{3})$ $Arg(z)=arctan((-1)/(-3))=arctan(1/3)$

However, z found in 3rd quadrant. Hence,

$z = \sqrt{10} \cdot C i s (π + arctan (\frac{1}{3}))$ $z=sqrt10*Cis(pi+arctan(1/3))$

How do you write the complex number in trigonometric form −3−i-3-i?