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April 19, 2015

Homework Help: PURE MATHEMATICS

Posted by Kerry-Ann on Friday, September 13, 2013 at 6:25pm.

1. The complex number 'a' is such that a^2=5-12i
use an algebraic method to find the two possible values of 'a'

8. The complex number z is given by z=cosTheta + isinTheta where -1/2pi< or equal to Theta less than or equal to 1/2pi.

a. show that |1+z|=2cos(1/2Theta) and arg(1+z)=1/2Theta.

b. hence, show that 1/(1+z)=1/2[1-itan(1/2Theta)]

c. describe the locus of the point representing z and the locus of the point representing 1/(1+z) in an argand diagram as Theta varies from -pi/2 to pi/2

9. A) find the exact value of all the roots of the equation (z+2+5i)(z^2+2z+5)=0

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