Question

Convert the complex number 3 + 3i into its polar representation.

Answer 1

Answer:

3 sqrt(2)(cos 45 degrees + i sin 45 degrees)

Step-by-step explanation:

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Answer 2

Answer:

$z=3(cos 45^{\circ} + i sin 45^{\circ})$

Step-by-step explanation:

The given complex number is:

$z=3+3i$

First of all, we find the modulus of the complex number.

Given a complex number written in the form

$z=a+ib$

The modulus is given by

$\rho =\sqrt{a^2+b^2}$

Here we have:

a = 3

b = 3

So the modulus is

$\rho=\sqrt{3^2+3^2}=3$

Now we find the argument. The argument is given by the equation:

$tan \theta = \frac{b}{a}$

In this case,

a = 3

b = 3

So the argument is:

$\theta=tan^{-1}(\frac{3}{3})=45^{\circ}$

So we can rewrite the complex number using polar representation as:

$z=\rho (cos \theta + i sin \theta)$

So

$z=3(cos 45^{\circ} + i sin 45^{\circ})$