## Complex Numbers - Polar form - IB math HL

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### Complex Numbers - Polar form - IB math HL

Convert from Cartesian form to polar form- Complex numbers - IB Mathematics HL

How can we express the complex number $z=1+\sqrt{3}i$ in polar form?

Thanks
Brynlee

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm

### Re: Complex Numbers - Polar form - IB math HL

Cartesian form to polar form- Complex numbers - IB Maths HL

In this case the argument $\theta$ of the complex number $z=1+\sqrt{3}i$ is

$\theta = arctan(\frac{\sqrt{3}}{1})=\frac{\pi}{3}$

and the modulus equals to

$|z| =\sqrt{1^2+(\sqrt{3})^2}=2$

So the complex number $1+\sqrt{3}i$ can be written in polar form as following

$z= 2(cos ( \frac{\pi}{3}) + isin( \frac{\pi}{3}))$

Hope these help!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### Re: Complex Numbers - Polar form - IB math HL

Thank you!!
Brynlee

Posts: 0
Joined: Mon Jan 28, 2013 8:10 pm