convert the following complex number into its polar representation 2+2i

To write 2+2i into polar form we proceed as follows:
2+2i
simplifying the above we get
2(1+i)
dividing through above through by √2
=2*√2(1/√2+i/√2)
but
1/√2=cos (π/4)=sin (π/4)
thus our expression will be:
=2√2(cos (π/4)+isin (π/4))

Answer Link

boffeemadrid boffeemadrid · Answer 2 · 2019-05-07T09:24:56+02:00

Answer:

[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]

Step-by-step explanation:

The given complex number is:

[tex]2+2i[/tex]

Now, the polar from of the complex number [tex]z=a+ib[/tex] is [tex]z=r(cos{\theta}+isin{\theta})[/tex].

Finding the absolute value of r:

[tex]r=|z|={\sqrt{2^2+2^2}[/tex]

[tex]r=\sqrt8[/tex]

[tex]r=2\sqrt{2}[/tex]

Now, find the value of argument,

Using formula, [tex]{\theta}=tan^{-1}(\frac{b}{a})[/tex]

[tex]{\theta}=tan^{-1}({\frac{2}{2})[/tex]

[tex]{\theta}=tan^{-1}(1)[/tex]

[tex]{\theta}={\frac{\pi}{4}}[/tex]

Thus, the polar form is:

[tex]z=2\sqrt{2}(cos{\frac{\pi}{4}}+isin{\frac{\pi}{4}})[/tex]

which is the required polar form.