Hello .
i'm struggling through A level math. Anw, i had a problem with Complex. :| I watched the key and i understant it but i still want to know what i was wrong. Help me.
If ( sqrt3 -i) is a root of the equation Z^9 + 16( 1+i) z^3 +g +ih=0
(sqrt3-i)^3 =-8i
Let z ^2 = t => the equation: t^2 +16 (1+i)t +g +ih =0.
Then i solve it. But i got the wrong answer
Is finding the other roots what you are trying to do? Anyway, it should be
z^3 = t => t^3+16(1+i)t+g+ih=0
Hi,
I believe the question you raised is not complete. Let us assume that we are finding the values of g and h. This type of question is common and it has appeared in the Nov 2008 H2 Maths exam.
We are given sqrt(3) - i is a root, so z = sqrt(3) - i must satisfy the equation
z^9 + 16(1 + i)(z^3) + g + hi = 0.
Consider z^3, this gives us -8i, which is easier for us to deal with.
Now our original equation can be seen equivalent as
(z^3)^2 + 16(1 + i)(z^3) + g + hi = 0.
Substituting z^3 = -8i, we obtain
(-8i)^2 + 16(1 + i)(-8i) + g + hi = 0
-64 + 16(-8i + 8) + g + hi = 0.
Comparing real parts, we get
-64 + 128 + g = 0
g = -64.
Comparing imaginary parts, we get
-128 + h = 0
h = 128.
Thanks.
Cheers,
Wen Shih
wenshih.wordpress.com
ah ha. I got it. Thank you
Hm. I have a question.
How can we find the smallest distance between 2 skew line?
Originally posted by Theplayfulgirl brainy:Hm. I have a question.
How can we find the smallest distance between 2 skew line?
Choose any point on the first skew line, and any point on the second skew line. For a vector with it, and find the length of projection onto the line perpendicular (cross the directional vectors of both skew lines) to both skew lines
Hi,
That is not in syllabus, although some schools continue to ask in exams.
Thanks.
Cheers,
Wen Shih