Question

Convert the complex number 2√3+0i into polar form. Express the angle using radians in terms of π over the interval

0≤θ<2π.

Answer 1

To convert the complex number 2√3 + 0i into polar form, the magnitude can be found using the formula √(a^2 + b^2), and the angle can be found using the formula arctan(b/a). Using these formulas, the polar form of the complex number 2√3 + 0i is 2√3.

Step-by-step explanation:

To convert the complex number 2√3 + 0i into polar form, we can use the formula:

r = √(a^2 + b^2)

where a is the real part and b is the imaginary part of the complex number. In this case, a = 2√3 and b = 0. Therefore, r = √((2√3)^2 + 0^2) = 2√3.

The angle, θ, can be found using the formula:

θ = arctan(b/a)

In this case, b = 0 and a = 2√3. Therefore, θ = arctan(0/(2√3)) = 0.

So, the polar form of the complex number 2√3 + 0i is 2√3 cis(0π) or 2√3.