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Description: Find the quotient21/22 in standard form.Convert to trig onometric form and findthe guotient to check your anduer,2,=-4, 2=2.000

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Find the quotient 2ı/22 in standard form Convert to trig onometric form and find the guotient to check your anduer, 2,=-4, 22=2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.5: Trigonometric Form For Complex Numbers

Problem 68E

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Topic Video

Question

Find the quotient
21/22 in standard form.
Convert to trig onometric form and find
the guotient to check your anduer,
2,=-4, 2=2.
000

Expert Solution

Step 1

It is given that $z_{1} = - 4, z_{2} = 2$ .

Substitute $z_{1} = - 4, z_{2} = 2$ in $\frac{z_{1}}{z_{2}}$ :

$\frac{z_{1}}{z_{2}} = \frac{- 4}{2} \frac{z_{1}}{z_{2}} = - 2$

Step 2

Convert to trigonometric form to check the answer as follows:

Note that $z_{1} = - 4$ which can be written as,

$x + i y = - 4 \Rightarrow x = - 4, y = 0$

Substitute $x = - 4, y = 0$ in $r = \sqrt{x^{2} + y^{2}}$ :

$r = \sqrt{{(- 4)}^{2} + 0^{2}} r = \sqrt{16} r = 4$

Note that,

$\cos θ = \frac{x}{r} \cos θ = \frac{- 4}{4} \cos θ = 1 \sin θ = \frac{y}{r} \sin θ = \frac{0}{4} \sin θ = 0$

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