- #1

- 60

- 8

- Homework Statement:
- Help me with this Algebra problem?

- Relevant Equations:
- None.

Below is the problem and the correct answer for this algebra problem is 7√2. But I cannot get to the correct answer.

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- Thread starter Math100
- Start date

- #1

- 60

- 8

- Homework Statement:
- Help me with this Algebra problem?

- Relevant Equations:
- None.

Below is the problem and the correct answer for this algebra problem is 7√2. But I cannot get to the correct answer.

Last edited by a moderator:

- #2

member 587159

(1) This is no linear algebra.

(2) Please type out what's written in the images.

(2) Please type out what's written in the images.

- #3

- 60

- 8

abs((21+7i)/(1-2i))=a√b where a=_____ and b=_____.

- #4

Office_Shredder

Staff Emeritus

Science Advisor

Gold Member

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What have you tried to do so far?

- #5

Keith_McClary

Gold Member

- 616

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Can you calculate ##(1+2i)(1-2i)## and use that to calculate ##\frac{1}{1-2i}##?

- #6

FactChecker

Science Advisor

Gold Member

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PS. I think it would be easier to start with the fact that |z1/z2| = |z1| / |z2| and apply the Pythagorean theorem to both the numerator and the denominator separately.

- #7

- 960

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You already found ##x+yi##. The problem asks you for ##|x+yi|##, so the next step should be straight-forward.

- #8

Mark44

Mentor

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- 6,878

The original post has nothing to do with Linear Algebra.

- #9

Mark44

Mentor

- 35,132

- 6,878

The 2nd image in post #1 shows what the OP has tried.What have you tried to do so far?

The OP did this in the 2nd image.Can you calculate ##(1+2i)(1-2i)## and use that to calculate ##\frac{1}{1-2i}##?

- #10

- 60

- 8

You already found ##x+yi##. The problem asks you for ##|x+yi|##, so the next step should be straight-forward.

- #11

- 60

- 8

Thank you so much for the hint. I was able to solve the problem with your hint.

- #12

- 960

- 67

Thank you so much for the hint. I was able to solve the problem with your hint.

Sorry for the late reply. Your work looks alright. But it might help, in the future, to show a little bit more detail than this. The answer would be clearer to the grader if you had written something like:

\begin{align*}

\sqrt{\frac{49}{25}+\frac{2401}{25}}&=\sqrt{\frac{1}{25}(49+2401)}\\

&=\sqrt{\frac{1}{25}(2450)}\\

&=\sqrt{\frac{1}{25}\cdot (2\cdot 25\cdot 49)}\\

&=\sqrt{(\frac{1}{25}\cdot 25)(2\cdot 49)}\\

&=\sqrt{2\cdot 49}\\

&=\sqrt{2\cdot 7^2}\\

&=\sqrt{2}\cdot \sqrt{7^2}\\

&=7\sqrt{2}

\end{align*}

- #13

FactChecker

Science Advisor

Gold Member

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A simplification is to factor out as much as you can as soon as you can and use the basic properties of the modulus:

|(21+7i)/(1+2i)|

=|21+7i|/|1+2i|

= 7*|3+i|/|1+2i|

= 7*##\sqrt {10}##/##\sqrt 5##

= 7*##\sqrt 5 ## * ##\sqrt 2##/##\sqrt 5##

= 7##\sqrt 2##

EDIT: PS. You can often do these things in homework and exam problems that are "rigged" (for one thing, so that the teacher is sure that he has the right answer.) It is not so common in real-world problems.

|(21+7i)/(1+2i)|

=|21+7i|/|1+2i|

= 7*|3+i|/|1+2i|

= 7*##\sqrt {10}##/##\sqrt 5##

= 7*##\sqrt 5 ## * ##\sqrt 2##/##\sqrt 5##

= 7##\sqrt 2##

EDIT: PS. You can often do these things in homework and exam problems that are "rigged" (for one thing, so that the teacher is sure that he has the right answer.) It is not so common in real-world problems.

Last edited:

- #14

- 60

- 8

Sorry for the late reply. Your work looks alright. But it might help, in the future, to show a little bit more detail than this. The answer would be clearer to the grader if you had written something like:

\begin{align*}

\sqrt{\frac{49}{25}+\frac{2401}{25}}&=\sqrt{\frac{1}{25}(49+2401)}\\

&=\sqrt{\frac{1}{25}(2450)}\\

&=\sqrt{\frac{1}{25}\cdot (2\cdot 25\cdot 49)}\\

&=\sqrt{(\frac{1}{25}\cdot 25)(2\cdot 49)}\\

&=\sqrt{2\cdot 49}\\

&=\sqrt{2\cdot 7^2}\\

&=\sqrt{2}\cdot \sqrt{7^2}\\

&=7\sqrt{2}

\end{align*}

Thank you so much for the help!

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