What is the trigonometric form of $(3 + 6 i)$ $(3+6i)$ ?

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Answer 1 · 2018-05-15T22:47:35

$z = 3 \sqrt{5} (cos ({63.43}^{\circ}) + i sin ({63.43}^{\circ}))$ $z= 3sqrt5(cos(63.43^@)+isin(63.43^@))$

Determine $r$ $r$
$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$

$r = \sqrt{45} = 3 \sqrt{5}$ $r=sqrt(45)=3sqrt5$

To find $θ$ $theta$
$θ = arctan (\frac{b}{a})$ $theta= arctan(b/a)$
$θ = arctan (\frac{6}{3}) = {63.43}^{\circ}$ $theta= arctan(6/3)=63.43^@$

In trigonometric form:
$z = 3 \sqrt{5} (cos ({63.43}^{\circ}) + i sin ({63.43}^{\circ}))$ $z= 3sqrt5(cos(63.43^@)+isin(63.43^@))$

What is the trigonometric form of (3+6i) (3+6i) ?