Mathematics 25 Online
OpenStudy (anonymous):

complex numbers anyone?

OpenStudy (anonymous):

$z=(1+i \sqrt{3})^{-2}$ how do i write z in modulus .... and argument form?

OpenStudy (anonymous):

I'm not familiar with those forms, but I would just use the negative exponent to drop it to the denominator.. Then multiply top/bottom by the square of the conjugate and simplify.

OpenStudy (anonymous):

the argument is 2pi/3 and mod= 1/4 so$\frac14<2\pi /3$

OpenStudy (anonymous):

I could be completely wrong though

OpenStudy (anonymous):

Oh I see. Euler notation.

OpenStudy (anonymous):

if z is a complex no. written by $z=r <\theta$then z^2 is given by $z^2=r^2< 2 \theta$

OpenStudy (anonymous):

no wonder i coulddn't work it out... i hadn't been taught that name as a notation either.

OpenStudy (anonymous):

here $z=\frac1{1+\sqrt3i}$ so $r=1/\sqrt{1+3}=1/2$$\theta= \tan^{-1}\frac{\sqrt3}1=\frac {\pi}3$ so you have z^2 and u nedd to make square of r and 2 theta $(1+\sqrt3i){^-2}=\frac14 < \frac {2\pi }3$

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