How do you convert $1 - 3 i$ $1 - 3i$ to polar form?

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How do you convert $1 - 3 i$ $1 - 3i$ to polar form?

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Answer 1 · 2018-06-24T06:18:52

$Polar form = (r, θ) = (3.1623, {288.43}^{\circ}$ $color(purple)("Polar form "= (r, theta) = (3.1623, 288.43^@$

Explanation:

$z = 1 - i 3$ $z = 1 - i 3$

$r = \sqrt{1^{2} + {(- 3)}^{2}} = \sqrt{10} = 3.1623$ $r = sqrt (1^2 + (-3)^2) = sqrt 10 = 3.1623$

$θ = {tan}^{- 1} (- \frac{3}{1}) = - {71.57}^{\circ} = {288.43}^{\circ}, as point lies in IV quadrant$ $theta = tan ^(-1) (-3/1) = -71.57^@ = 288.43^@, " as point lies in IV quadrant"$

$Polar form = (r, θ) = (3.1623, {288.43}^{\circ}$ $color(purple)("Polar form "= (r, theta) = (3.1623, 288.43^@$

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How do you convert $1 - 3 i$ $1 - 3i$ to polar form?

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