## Complex Numbers polar form

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### Complex Numbers polar form

Complex Numbers, Cartesian to polar form - IB Mathematics HL

How can we express the complex number $z=1- \sqrt3 i$ in polar form?

Thanks
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

### Re: Complex Numbers polar form

The argument $\theta$ of a complex number $z=a+ib$

is given by the formula:

$\theta = arctan(\frac{b}{a}$

and the modulus

$|z| =\sqrt{a^2+b^2}$

and the polar form will be

$z= |z|(cos \theta +isin \theta)= |z|cis( \theta)$

in your question

$\theta = arctan(\frac{-\sqrt3}{1}= -\frac{\pi}{3}$

and the modulus is given by the following formula:

$|z| =\sqrt{1^2+(-\sqrt3)^2}$

$|z| =\sqrt{1+3}=\sqrt{4}=2$

$z= |z|(cos ( -\frac{\pi}{3}) +isin( -\frac{\pi}{3}))= 2cis(- \frac{\pi}{3})$
lily

Posts: 0
Joined: Mon Jan 28, 2013 8:04 pm

### Re: Complex Numbers polar form

Thanks Lily!!
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

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