# Dividing Complex Numbers

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Feb 20, 2022.

1. ### nycmathguy

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Section 6.6

nycmathguy, Feb 20, 2022
2. ### MathLover1

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you have
, that is incorrect

need to do this way:

=

=...........rationalize

=

=

=

=0.086824+0.492405*i

you did same mistake with

do it like I did above and result should be:
-0.735626 +1.01062*i

Last edited: Feb 21, 2022
MathLover1, Feb 21, 2022
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3. ### nycmathguy

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Did I get both questions wrong? What error did I make twice?

nycmathguy, Feb 21, 2022
4. ### MathLover1

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yes

MathLover1, Feb 21, 2022
5. ### nycmathguy

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What error did I make twice?

nycmathguy, Feb 21, 2022
6. ### MathLover1

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you cannot factor out 1/2 and write cos and sin as difference of angles from numerator and denominator
that is WRONG

compare to (cos(x)+sin(x))/(cos(y)+sin(y))-> you cannot write it as cos(x-y)+sin(x-y)

MathLover1, Feb 21, 2022
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7. ### nycmathguy

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Let me post what Ron Larson said to do. BRB.

nycmathguy, Feb 22, 2022
8. ### nycmathguy

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nycmathguy, Feb 22, 2022
9. ### MathLover1

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that is new to me, I do not recall that method but it's much shorter (I was always doing rationalization)

I know the theorem for division of complex numbers is:

Let $$z1=(r1,θ1)$$ and $$z2=(r2,θ2)$$ be complex numbers expressed in polar form, such that z2≠0.

Then:
$$z1/z2=r1/r2(cos(θ1-θ2)+i*sin(θ1-θ2))$$

Proof
$$z1/z2 =r1(cosθ1+isinθ1/r2(cosθ2+isinθ2)$$.Definition of Polar Form of Complex Number

=$$(r1(cosθ1+isinθ1))(r2(cosθ2−isinθ2))(r2(cosθ2+isinθ2)(r2(cosθ2−isinθ2))$$.multiplying numerator and denominator by $$r2(cosθ1-isinθ1)$$

=$$r1r2(cos(θ1−θ2)+isin(θ1−θ2))/(r2^2(cos(θ2−θ2)+isin(θ2θ2))$$.Product of Complex Numbers in Polar Form

=$$(r1(cos(θ1−θ2)+isin(θ1−θ2)))/(r2(cos0+isin0))$$

=$$(r1/r2)(cos(θ1−θ2+isin(θ1-θ2))$$ ........Cosine of Zero is One and Sine of Zero is Zero

Last edited: Feb 22, 2022
MathLover1, Feb 22, 2022
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10. ### nycmathguy

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Is Larson wrong?

nycmathguy, Feb 22, 2022
11. ### MathLover1

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this is a result using wolfram alpha

MathLover1, Feb 22, 2022
12. ### nycmathguy

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What do I do? Unfortunately, the answers to even number problems are not listed in the back of the book as you already know. In that case, why not do 41 and 43? I will then check the answer listed on the back of the book by Larson. Sounds good?

nycmathguy, Feb 22, 2022
13. ### MathLover1

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ok

MathLover1, Feb 22, 2022
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14. ### Country Boy

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To divide $\frac{a+ bi}{c+ di}$, multiply both numerator and denominator by the conjugate of the denominator:

Country Boy, Feb 22, 2022

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