1. ## help

Calculate the amount lzl of the complex number

would glad if u guys could give me exemple because i cant find what lzl is

2. ## Re: help

Represent z as $\displaystyle a+bi$; then $\displaystyle |z|=\sqrt{a^2+b^2}$. See here for multiplication and division on complex numbers.

3. ## Re: help

Originally Posted by Petrus
Calculate the amount lzl of the complex number

would glad if u guys could give me exemple because i cant find what lzl is
Start by simplifying so that it is in z = a + bi form.

4. ## Re: help

so a = (9+2i)(7+6i) and b = (7+2i)(-7+7i)?

5. ## Re: help

No, first begin by simplifying the numerator:

$\displaystyle (9+2i)(7+6i)=63+54i+14i+12i^2=51+68i$

Then do the same for the denominator, then factor out any constants and multiply the simplified ratio by the conjugate of the denominator to get the original ratio in the form a + bi.

6. ## Re: help

ok now i got (51+68i)/(-63+35i) so next is to multiplicate with (-63-35i)?

7. ## Re: help

"Multiplicate"? Multiply both numerator and denominator by -63- 35i.
(I didn't check to see if that fraction is actually correct.)

8. ## Re: help

can u check if it is, im not really that good, but i cant see how i can get this to a+bi forme

9. ## Re: help

Yes, that is correct. So you now have:

$\displaystyle \frac{51+68i}{-63+35i}=\frac{1}{7}\cdot\frac{51+68i}{-9+5i}$

We factor out the 7 from the denominator to help keep the computations simple.

So, multiply the complex fraction by the conjugate of the denominator:

$\displaystyle \frac{1}{7}\cdot\frac{51+68i}{-9+5i}\cdot\frac{-9-5i}{-9-5i}$

This will cause the denominator to be real, and you will then have the complex number in rectangular form.

10. ## Re: help

Originally Posted by Petrus
Calculate the amount lzl of the complex number
would glad if u guys could give me exemple because i cant find what lzl is
Make it easy. Just calculate $\displaystyle \frac{|9+2i||7+6i|}{|7+2i||-7+7i|}~.$

11. ## Re: help

Originally Posted by Plato
Make it easy. Just calculate $\displaystyle \frac{|9+2i||7+6i|}{|7+2i||-7+7i|}~.$
But is it easier to evaluate four moduli then multiply/divide them, or to simplify to a single complex number and taking the modulus?