What is the trigonometric form of $5 + 6 i$ $5+6i$ ?

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What is the trigonometric form of $5 + 6 i$ $5+6i$ ?

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Answer 1 · 2016-02-28T21:59:47

$\sqrt{61} [cos (0.876) + i sin (0.876)]$ $sqrt61[cos(0.876) + isin(0.876)]$

Explanation:

using the following formulae.

$∙ r^{2} = x^{2} + y^{2}$ $• r^2 = x^2 + y^2$

$∙ θ = {tan}^{- 1} (\frac{y}{x})$ $• theta = tan^-1 (y/x)$

here x = 5 and y = 6

$r^{2} = 5^{2} + 6^{2} = 25 + 36 = 61 \Rightarrow r = \sqrt{61}$ $r^2 = 5^2+6^2 = 25+36 = 61 rArr r = sqrt61$

$θ = {tan}^{- 1} (\frac{6}{5}) \approx 0.876 radians$ $theta = tan^-1(6/5) ≈ 0.876 " radians "$

hence the trig. form of 5 + 6i is:

$\sqrt{61} [cos (0.876) + i sin (0.876)]$ $sqrt61[ cos(0.876) + isin(0.876)]$

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What is the trigonometric form of $5 + 6 i$ $5+6i$ ?

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What is the trigonometric form of 5+6i5+6i?

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What is the trigonometric form of $5 + 6 i$ $5+6i$ ?