# Complex No. Qns

• Aug 3rd 2009, 03:23 PM
Chris0724
Complex No. Qns
hi ,

i got a question on complex no. How to prove the question is correct?

| (3 + j4)^5 | = 5^5
| ( 1 + j 3 ) | 2

i know that |Z| = |x + jy| = sqrt (x^2 + y^2) = ( Z x Z*)

for the lower part , i achieve ( 1 + 3 ) = 4 using ( Z x Z*) which i think i am right

but i am stuck on the upper part. can't acheive the answer..

(3 + j4)^5 which i can determine the r = 5 but am i on the right track converting into euler form ?

Thanks a lot for any help :)
• Aug 3rd 2009, 05:34 PM
Prove It
Quote:

Originally Posted by Chris0724
hi ,

i got a question on complex no. How to prove the question is correct?

| (3 + j4)^5 | = 5^5
| ( 1 + j 3 ) | 2

i know that |Z| = |x + jy| = sqrt (x^2 + y^2) = ( Z x Z*)

for the lower part , i achieve ( 1 + 3 ) = 4 using ( Z x Z*) which i think i am right

but i am stuck on the upper part. can't acheive the answer..

(3 + j4)^5 which i can determine the r = 5 but am i on the right track converting into euler form ?

Thanks a lot for any help :)

Show that
$\displaystyle \left|\frac{(3 + 4j)^5}{1 + 3j}\right| = \frac{5^5}{2}$?
• Aug 3rd 2009, 05:48 PM
songoku
Hi Chris0724

Quote:

Originally Posted by Chris0724
i know that |Z| = |x + jy| = sqrt (x^2 + y^2) = ( Z x Z*)

This should be : |Z| = |x + jy| = sqrt (x^2 + y^2) = sqrt ( Z x Z*)

Quote:

for the lower part , i achieve ( 1 + 3 ) = 4 using ( Z x Z*) which i think i am right
Maybe you want to recalculate this one ^^

Quote:

(3 + j4)^5 which i can determine the r = 5 but am i on the right track converting into euler form ?
Yes, r = 5 is right. You don't have to state it in euler form if you want to find |(3 + j4)^5|

But I don't think the question is right...
• Aug 3rd 2009, 09:12 PM
yeongil
Maybe this is the question?
$\displaystyle \frac{|(3 + 4j)^5|}{|1 + j{\color{red}\sqrt{3}}|} = \frac{5^5}{2}$

01
• Aug 4th 2009, 12:15 AM
songoku
Hi yeongil

I believe so ^^
• Aug 4th 2009, 01:09 AM
Chris0724
Quote:

Originally Posted by yeongil
Maybe this is the question?
$\displaystyle \frac{|(3 + 4j)^5|}{|1 + j{\color{red}\sqrt{3}}|} = \frac{5^5}{2}$

01

hi yes!! sorry for the typo error!! the question should be as above :)

and yes! it should have been sqrt (Z x Z*)

thanks!