What is the trigonometric form of $(- 5 + 11 i)$ $(-5+11i)$ ?

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What is the trigonometric form of $(- 5 + 11 i)$ $(-5+11i)$ ?

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Answer 1 · 2016-01-09T08:50:47

$\sqrt{146} (cos ({tan}^{- 1} (- \frac{11}{5})) + i sin ({tan}^{- 1} (- \frac{11}{5})))$ $sqrt(146)(cos(tan^-1(-11/5))+isin(tan^-1(-11/5)))$

Explanation:

Trigonometric form of a complex number $x + i y$ $x+iy$ is given by

$r (cos (θ) + i sin (θ)$ $r(cos(theta)+isin(theta)$
Where,
$r = \sqrt{x^{2} + y^{2}}$ $r=sqrt(x^2+y^2)$
$θ = {tan}^{- 1} (\frac{y}{x})$ $theta = tan^-1(y/x)$

Our complex number is $- 5 + 11 i$ $-5+11i$

$r = \sqrt{{(- 5)}^{2} + 11^{2}}$ $r=sqrt((-5)^2+11^2)$
$r = \sqrt{25 + 121}$ $r=sqrt(25+121)$
$r = \sqrt{146}$ $r=sqrt(146)$

$θ = {tan}^{- 1} (- \frac{11}{5})$ $theta = tan^-1(-11/5)$

The complex number in trigonometric form is

$\sqrt{146} (cos ({tan}^{- 1} (- \frac{11}{5})) + i sin ({tan}^{- 1} (- \frac{11}{5})))$ $sqrt(146)(cos(tan^-1(-11/5))+isin(tan^-1(-11/5)))$

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What is the trigonometric form of $(- 5 + 11 i)$ $(-5+11i)$ ?

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Explanation:

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Science

Math

Humanities

... and beyond

What is the trigonometric form of (−5+11i) (-5+11i) ?

1 Answer

Explanation:

Related questions

Impact of this question

What is the trigonometric form of $(- 5 + 11 i)$ $(-5+11i)$ ?