What is the trigonometric form of $(- 6 + 8 i)$ $(-6+8i)$ ?

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What is the trigonometric form of $(- 6 + 8 i)$ $(-6+8i)$ ?

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Answer 1 · 2018-06-15T10:24:09

$10 ({cos 126.87}^{\circ} + i {sin 126.87}^{\circ})$ $10(cos126.87^@+isin126.87^@)$

Explanation:

$the trigonometric form of a complex number is$ $"the trigonometric form of a complex number is"$

$∙ x r (cos θ + i sin θ) where$ $•color(white)(x)r(costheta+isintheta)" where"$

$∙ x r = \sqrt{x^{2} + y^{2}}$ $•color(white)(x)r=sqrt(x^2+y^2)$

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

$- 6 + 8 i \to x = - 6 and y = 8$ $-6+8itox=-6" and "y=8$

$r = \sqrt{{(- 6)}^{2} + 8^{2}} = \sqrt{100} = 10$ $r=sqrt((-6)^2+8^2)=sqrt100=10$

$- 6 + 8 i is in the second quadrant so θ must be$ $-6+8i" is in the second quadrant so "theta" must be"$
$an angle in the second quadrant$ $"an angle in the second quadrant"$

$θ = {tan}^{- 1} (\frac{4}{3}) = {53.13}^{\circ} \leftarrow related acute angle$ $theta=tan^-1(4/3)=53.13^@larrcolor(red)"related acute angle"$

$θ = {(180 - 53.13)}^{\circ} = {126.87}^{\circ} \leftarrow in second quadrant$ $theta=(180-53.13)^@=126.87^@larrcolor(red)"in second quadrant"$

$- 6 + 8 i = 10 ({cos 126.87}^{\circ} + i {sin 126.87}^{\circ})$ $-6+8i=10(cos126.87^@+isin126.87^@)$

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What is the trigonometric form of $(- 6 + 8 i)$ $(-6+8i)$ ?

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Science

Math

Humanities

... and beyond

What is the trigonometric form of (−6+8i) (-6+8i) ?

1 Answer

Explanation:

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Impact of this question

What is the trigonometric form of $(- 6 + 8 i)$ $(-6+8i)$ ?