Find the imaginary part of\[(\cos12^\circ+i\sin12^\circ+\co s48^\circ+i\sin48^\circ)^6.\]

The imaginary part is 0

Step-by-step explanation:

The number given is:

First, we can expand this power using the binomial theorem:

After that, we can apply De Moivre's theorem to expand each summand:

The final step is to find the common factor of i in the last expansion. Now:

The last part is to multiply these factors and extract the imaginary part. This computation gives:

(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)

A calculator simplifies the imaginary part Im(x⁶) to 0

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

it is b)

hope this : )

step-by-step explanation: