Question

What is the polar form of 7√3 - 7i?

A) 14(cos(30°) + i sin(30°))
B) 14(cos(60°) + i sin(60°))
C) 14(cos(90°) + i sin(90°))
D) 14(cos(120°) + i sin(120°))

Answer 1

The polar form of the complex number 7√3 - 7i is 14(cos(30°) + i sin(30°)).

Step-by-step explanation:

The polar form of the complex number 7√3 - 7i can be found by converting it to polar form which is given by:

z = r(cos(θ) + i sin(θ))

where r is the magnitude of the complex number and θ is the argument or angle in radians.

In this case, the magnitude can be found using the formula:

|z| = √(Re(z)² + Im(z)²)

Let's calculate the magnitude:

|z| = √((7√3)² + (-7)²) = √(147 + 49) = √196 = 14

The argument θ can be found using the formula:

θ = atan(Im(z)/Re(z))

Let's calculate the argument:

θ = atan(-7/(7√3)) = atan(-1/√3) = atan(-√3/3)

Now we can write the polar form as:

z = 14(cos(atan(-√3/3)) + i sin(atan(-√3/3)))

The correct polar form is option A) 14(cos(30°) + i sin(30°)).