How do you express the complex number in rectangular form: $z = 5 (cos 120 d e g r e e s + i sin 120 d e g r e e s)$ $z=5(cos 120degrees + i sin 120 degrees)$ ?

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How do you express the complex number in rectangular form: $z = 5 (cos 120 d e g r e e s + i sin 120 d e g r e e s)$ $z=5(cos 120degrees + i sin 120 degrees)$ ?

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Answer 1 · 2016-02-18T15:28:38

$(- \frac{5}{2}, \frac{5}{2} \sqrt{3})$ $(-5/2 , 5/2sqrt3 )$

Explanation:

using the formulae that links Polar to Rectangular coordinates.

$∙ x = r cos θ$ $• x = rcostheta$

$∙ y = r sin θ$ $• y = rsintheta$

here r = 5 and $θ = 120^{\circ}$ $theta = 120^@$

hence : $x = 5 {cos 120}^{\circ} = 5 \times - \frac{1}{2} = - \frac{5}{2}$ $x = 5cos120^@ = 5 xx -1/2 = -5/2$

and $y = 5 {sin 120}^{\circ} = 5 \times \frac{\sqrt{3}}{2} = \frac{5}{2} \sqrt{3}$ $y = 5sin120^@ = 5 xxsqrt3/2 = 5/2 sqrt3$

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How do you express the complex number in rectangular form: $z = 5 (cos 120 d e g r e e s + i sin 120 d e g r e e s)$ $z=5(cos 120degrees + i sin 120 degrees)$ ?

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Explanation:

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How do you express the complex number in rectangular form: z=5(cos 120degrees + i sin 120 degrees)z=5(cos120degrees+isin120degrees)z=5(cos 120degrees + i sin 120 degrees)?

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Explanation:

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How do you express the complex number in rectangular form: $z = 5 (cos 120 d e g r e e s + i sin 120 d e g r e e s)$ $z=5(cos 120degrees + i sin 120 degrees)$ ?