Question

Convert 2rad3 +2i into its polar form

Answer 1

2rad3?

Answer 2

\[2\sqrt 3 +2i\]
is this your problem?

Answer 3

Let z=2√3+2i comparing it with z=a+bi we find
a= 2√3, b= 2
Now
\[r=\sqrt{a^2+b^2} = \sqrt{(2\sqrt3)^2+2^2}= \sqrt{12+6}= \sqrt{16} = 4\]
\[\theta = \tan^{-1} (\frac{b}{a}) =\tan^{-1} (\frac{2}{2\sqrt3})=\tan^{-1} (\frac{1}{\sqrt3}) =30^0\]
Polar form of a complex number is given as
\[z=r(\cos \theta + i \sin \theta) \]
i.e. \[z=4(\cos30^0 + i \sin 30^0) \]
Which is the required polar form of the given complex number z=2√3+2i

Answer 4

Sorry, in the fourth line write 4 instead of 6