Multiply.
6√6cis(5π/9)⋅3√4cis(3π/4)
To multiply complex numbers in polar form, we can multiply their magnitudes and add their angles.
First, let's calculate the magnitudes:
6√6 * 3√4 = 18√(6*4) = 18√24 = 18√(4*6) = 18*2√6 = 36√6
Next, let's add the angles:
cis(5π/9) * cis(3π/4) = cis(5π/9 + 3π/4) = cis(20π/36 + 27π/36) = cis(47π/36)
So, the product is 36√6cis(47π/36)