Complex and Vectors

Theplayfulgirl brainy SG

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

8light SG

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

wee_ws SG

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

Theplayfulgirl brainy SG

ah ha. I got it. Thank you

Theplayfulgirl brainy SG

Hm. I have a question.

How can we find the smallest distance between 2 skew line?

eagle SG

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

wee_ws SG

Hi,

That is not in syllabus, although some schools continue to ask in exams.

Thanks.

Cheers,
Wen Shih