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# p4 complex numbers watch

1. i posted this in the maths forum with no replies... so i thought i'd give it a try here
thx
Ben

The complex number z has modulus 4 and argument pi/3
Find in the form a+bi,

(a) z^2
(b) 1/z
(c) i^3z

Don't worry. this isn't on any exam. Heinemann p4 pg 34 3B question 13
thx
2. z = 4(cos(pi/3) + i sin(pi/3)) = 2 + 2sqrt(3)i

z^2
= (2 + 2sqrt(3)i)^2
= 4 + 8sqrt(3)i - 12
= -8 + 8sqrt(3)i.

1/z
= 1/(2 + 2sqrt(3)i)
= [2 - 2sqrt(3)i] / [(2 + 2sqrt(3)i) (2 - 2sqrt(3)i)]
= [2 - 2sqrt(3)i] / 16
= 1/8 - (sqrt(3)/8)i.

(i^3)z
= (i^3) (2 + 2sqrt(3)i)
= (-i) (2 + 2sqrt(3)i)
= 2sqrt(3) - 2i.

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Updated: June 29, 2004
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