Question

Convert the polar representation of this complex number into its standard form: z=6(cos210 degrees isin210 degrees)

Answer 1

-6 + 6√3 * i.

Explanation:

The polar form of a complex number is given as z = r(cos θ + i sin θ), where r is the modulus and θ is the argument. In this case, z = 6(cos 210° + i sin 210°), so r = 6 and θ = 210°.

To convert the polar representation of z into its standard form, we can use the following formula:

z = r * cos θ + r * sin θ * i

Plugging in the values of r and θ, we get:

z = 6 * cos 210° + 6 * sin 210° * i

Evaluating the trigonometric functions, we get:

z = -6 + 6√3 * i

Therefore, the standard form of the complex number z is -6 + 6√3 * i.