Answer:
Explanation:
To express 6√3 + 6i in polar form, we first need to find the magnitude and argument of the complex number.
The magnitude (or modulus) of the complex number is given by the formula:
|z| = √(a^2 + b^2)
where a and b are the real and imaginary parts of the complex number, respectively.
In this case, a = 6√3 and b = 6, so:
|6√3 + 6i| = √((6√3)^2 + 6^2) = √(108 + 36) = √144 = 12
The argument (or angle) of the complex number is given by the formula:
arg(z) = tan^-1(b/a)
In this case, arg(z) = tan^-1(6/6√3) = tan^-1(1/√3) = π/6
Therefore, the polar form of 6√3 + 6i is:
12(cos(π/6) + i sin(π/6))
or
12e^(iπ/6)