What is the trigonometric form of $(- 4 + 3 i)$ $(-4+3i)$ ?

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What is the trigonometric form of $(- 4 + 3 i)$ $(-4+3i)$ ?

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Answer 1 · 2016-04-18T14:30:08

$5 cos θ + i 5 sin θ$ $5costheta+i5sintheta$ , where $θ = {tan}^{- 1} (- \frac{3}{4})$ $theta=tan^(-1)(-3/4)$

Explanation:

Trigonometric form of a complex number $a + b i$ $a+bi$ is $r cos θ + i sin θ$ $rcostheta+isintheta$ .

As such here, $r cos θ = - 4$ $rcostheta=-4$ and $r sin θ = 3$ $rsintheta=3$ .

Squaring the two and adding

$r^{2} ({cos}^{2} θ + {sin}^{2} θ) = {(- 4)}^{2} + 3^{2} = 16 + 9 = 25$ $r^2(cos^2theta+sin^2theta)=(-4)^2+3^2=16+9=25$

or $r^{2} = 25$ $r^2=25$ and $r = 5$ $r=5$

Dividing we get $\frac{r sin θ}{r cos θ} =$ $(rsintheta)/(rcostheta)=$ -3/4# or

$tan θ = - \frac{3}{4}$ $tantheta=-3/4$ or $θ = {tan}^{- 1} (- \frac{3}{4})$ $theta=tan^(-1)(-3/4)$

Hence $a + b i$ $a+bi$ in trigonometric form is $5 cos θ + i 5 sin θ$ $5costheta+i5sintheta$ , where $θ = {tan}^{- 1} (- \frac{3}{4})$ $theta=tan^(-1)(-3/4)$

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What is the trigonometric form of $(- 4 + 3 i)$ $(-4+3i)$ ?

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What is the trigonometric form of (−4+3i) (-4+3i) ?

1 Answer

Explanation:

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What is the trigonometric form of $(- 4 + 3 i)$ $(-4+3i)$ ?