+0

# Precalculus Question

0
870
5

Given Z = 2(cos 148º + isin 148º) and W = 5(cos 11º + isin 11º), find and simplify Z divided by W. Round numerical values to the nearest hundredth.

A)0.4(cos 137º - isin 137º)

B)0.4(cos 137º + isin 137º)

C)10(cos 137º - isin 137º)

D)10(cos 137º + isin 137º)

Guest Nov 24, 2014

### Best Answer

#2
+93352
+10

I have another method :)

$$cos\theta+isin\theta = e^{i\theta}\\\\$$

where theta is in radians

$$\\148^0=\frac{148\pi}{180}\; radians\\\\ 11^0=\frac{11\pi}{180}\; radians\\\\$$

Given Z = 2(cos 148º + isin 148º) and W = 5(cos 11º + isin 11º), find and simplify Z divided by W.

becomes

$$\\\dfrac{2e^{(148\pi/180)i}}{5e^{(11\pi/180)i}}\\\\ =0.4e^{[(148\pi/180)-(11\pi/180)]i}\\\\$$

$$\left({\frac{{\mathtt{148}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{180}}}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{11}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{180}}}}\right) = {\mathtt{2.391\: \!101\: \!075\: \!232\: \!231\: \!5}}$$

=0.4cos (2.3911010752322315) +0.4* isin(2.3911010752322315)

remember this is in radians.

= -0.2925 + 0.2728i

=  -0.29 + 0.27i

I think that method is correct.

Melody  Nov 25, 2014
#1
+17745
+10

If you have two complex numbers written in polar notation, for example:

A = a(cosα + i·sinα)     and     B = b(cosβ + i·sinβ)

Then A / B  =  (a/b)( cos(α - β) + i·sin(α - β) )

Can you see how to apply this?

geno3141  Nov 24, 2014
#2
+93352
+10
Best Answer

I have another method :)

$$cos\theta+isin\theta = e^{i\theta}\\\\$$

where theta is in radians

$$\\148^0=\frac{148\pi}{180}\; radians\\\\ 11^0=\frac{11\pi}{180}\; radians\\\\$$

Given Z = 2(cos 148º + isin 148º) and W = 5(cos 11º + isin 11º), find and simplify Z divided by W.

becomes

$$\\\dfrac{2e^{(148\pi/180)i}}{5e^{(11\pi/180)i}}\\\\ =0.4e^{[(148\pi/180)-(11\pi/180)]i}\\\\$$

$$\left({\frac{{\mathtt{148}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{180}}}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{11}}{\mathtt{\,\times\,}}{\mathtt{\pi}}}{{\mathtt{180}}}}\right) = {\mathtt{2.391\: \!101\: \!075\: \!232\: \!231\: \!5}}$$

=0.4cos (2.3911010752322315) +0.4* isin(2.3911010752322315)

remember this is in radians.

= -0.2925 + 0.2728i

=  -0.29 + 0.27i

I think that method is correct.

Melody  Nov 25, 2014
#3
+93352
0

How did you get your equation Geno.

I can see another method but you seem to have used a 3rd method

Melody  Nov 25, 2014
#4
+26973
+5

To answer your question Melody, use the following notation;

$$A=ae^{i\alpha}$$

$$B=be^{i\beta}$$

then

$$\frac{A}{B}=\frac{a}{b}e^{i(\alpha - \beta)}\rightarrow \frac{a}{b}(\cos(\alpha -\beta)+i\sin(\alpha - \beta))$$

.

Alan  Nov 25, 2014
#5
+93352
0

There you go.

I am practicing my philosophical approach.

Why do it the easy way if there is a long way that works just as well.    LOL

Thanks Alan.

Melody  Nov 25, 2014

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