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# Further Maths Complex Numbers Help :) Watch

1. The equation z^4 - 8z³ + 20z² - 72z + 99 = 0 has a pure imaginary root.
The root is z = +/- 3j

Solve the equation.

The answer is 4 +/- ? 5 but I have no idea how to get there.
I was going to try and make it (z² + ...)(z² - ....)=0 & use one so I could solve it using the quadratic formula but...nothing is working.

Any help is greatly appreciated!
2. Have you covered factor theorem yet?

They've given you two of the roots so you can use factor theorem to write (z+3i)(z-3i)(z^2 + Bz + C) = z^4 - 8z³ + 20z² - 72z + 99, then equate co-efficients
3. Sub in z = 0, then z = 1, then z = -1, then z = 2, then z = -2, until you find a root, f(z).

If (f-a) in z equals zero, then z = a.

Thus you will know one root, and the conjugate of it so two roots (z-a)(z+a)(Az^2 + Bz + C)

Find A, B, C.
4. Let me have a go..;D

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Updated: December 11, 2010
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