Math - Complex Numbers

Audi SG

1. Express (3-i)^2 in the form a + ib.

Hence or otherwise find the roots of the equation

(z + i)^2 = -8 + 6i

I am not sure how I can relate part one to part two. Need help over here.

2.The complex numberx z and w have moduli k and 3k^2 respectively and arguments alfa and 4alfa respectively. where k is a positive constant and -pi/4 < alfa < pi/4. Express in the form a + ib.

i) z^3

ii) z/w*

Basically I need help with part (ii). I manage to form the polar form of the expression but I got an angle of 5 alfa and I dont know how to find the basic angle.

Thanks for helping.

ThunderFbolt SG

1. the answer for (3-i)^2 = 8 - 6i (done via (a+b)^2 = a^2 + 2ab + b^2)

see the relation now?

wee_ws SG

Hi,

For Q1, also consider the fact that i^2 = -1.

Thanks.

Cheers,
Wen Shih

wee_ws SG

Hi,

For Q2, we will start with -5pi/4 < 5 alpha < 5pi/4.

Then we have to consider 3 cases:

1. 5 alpha is within the principal range.

2. 5 alpha is greater than pi.

3. 5 alpha is less than -pi.

Thanks.

Cheers,
Wen Shih