How do you write $\frac{1}{2} + 5 i$ $1/2+5i$ in polar form and find ?

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How do you write $\frac{1}{2} + 5 i$ $1/2+5i$ in polar form and find ?

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Answer 1 · 2016-02-12T10:59:04

$z = 5.025 \cdot (cos 1.47 + i sin 1.47)$ $z = 5.025* (cos 1.47 +isin 1.47)$ Angle expressed in radians.

Explanation:

In polar form $(\frac{1}{2} + 5 \cdot i)$ $(1/2+5*i)$ lies on the 1st quardrant. The length of it from the origin is $r = \sqrt{{.5}^{2} + 5^{2}} = \sqrt{25.25} = 5.025$ $r = sqrt(.5^2+5^2) = sqrt 25.25 = 5.025$ The argument is $θ = {tan}^{- 1} (\frac{5}{.5}) or θ = {tan}^{- 1} 10 = 1.47 r a d i a n$ $theta=tan^-1 (5/.5) or theta = tan^-1 10 = 1.47 radian$
So in Polar form $z = 5.025 \cdot (cos 1.47 + i sin 1.47)$ $z = 5.025* (cos 1.47 +isin 1.47)$ ; If $θ$ $theta$ is expressed in degree then $z = 5.025 \cdot (cos 84.29 + i sin 84.29)$ $z = 5.025* (cos 84.29 +isin 84.29)$

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How do you write $\frac{1}{2} + 5 i$ $1/2+5i$ in polar form and find ?

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