MATH SOLVE

2 months ago

Q:
# Find the quotient of the complex numbers

Accepted Solution

A:

Answer: [tex]\frac{2}{9}\left(\cos\left(\frac{\pi}{132}\right)+i*\sin\left(\frac{\pi}{132}\right)\right)[/tex]

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If the text is too small, then check out the attached image for a bigger version of the same answer

The answer written out in keyboard form is (2/9)*(cos(pi/132)+i*sin(pi/132))

=======================================

Work Shown:

z1 = a*(cos(b) + i*sin(b))

z1 = 2*(cos(pi/11) + i*sin(pi/11))

here we see that a = 2 and b = pi/11

z2 = c*(cos(d) + i*sin(d))

z2 = 9*(cos(pi/12) + i*sin(pi/12))

here we see that c = 9 and d = pi/12

----------------

Now use the rule

If

z = a*(cos(b) + i*sin(b)) and w = c*(cos(d)+i*sin(d))

then

z/w = (a/c)*(cos(b-d)+i*sin(b-d))

We have

a = 2

b = pi/11

c = 9

d = pi/12

So...

z/w = (a/c)*(cos(b-d)+i*sin(b-d))

(z1)/(z2) = (a/c)*(cos(b-d)+i*sin(b-d))

(z1)/(z2) = (2/9)*(cos(pi/11-pi/12)+i*sin(pi/11-pi/12))

(z1)/(z2) = (2/9)*(cos(12pi/132-11pi/132)+i*sin(12pi/132-11pi/132))

(z1)/(z2) = (2/9)*(cos(pi/132)+i*sin(pi/132))

which is the answer in polar form

Note: refresh the page if the symbols aren't showing up correctly

If the text is too small, then check out the attached image for a bigger version of the same answer

The answer written out in keyboard form is (2/9)*(cos(pi/132)+i*sin(pi/132))

=======================================

Work Shown:

z1 = a*(cos(b) + i*sin(b))

z1 = 2*(cos(pi/11) + i*sin(pi/11))

here we see that a = 2 and b = pi/11

z2 = c*(cos(d) + i*sin(d))

z2 = 9*(cos(pi/12) + i*sin(pi/12))

here we see that c = 9 and d = pi/12

----------------

Now use the rule

If

z = a*(cos(b) + i*sin(b)) and w = c*(cos(d)+i*sin(d))

then

z/w = (a/c)*(cos(b-d)+i*sin(b-d))

We have

a = 2

b = pi/11

c = 9

d = pi/12

So...

z/w = (a/c)*(cos(b-d)+i*sin(b-d))

(z1)/(z2) = (a/c)*(cos(b-d)+i*sin(b-d))

(z1)/(z2) = (2/9)*(cos(pi/11-pi/12)+i*sin(pi/11-pi/12))

(z1)/(z2) = (2/9)*(cos(12pi/132-11pi/132)+i*sin(12pi/132-11pi/132))

(z1)/(z2) = (2/9)*(cos(pi/132)+i*sin(pi/132))

which is the answer in polar form