Let z =8(cos (pi/3) + i sin (pi/3)) and w= 3(cos(pi/6) +isin (pi/6)

Which statement describes the geometric construction of the product zw on the complex plane?

No statements are given...

At the very least, we can compute the product zw by multiplying the moduli and adding the arguments. That is, if

z = 8 (cos(π/3) + i sin(π/3))

w = 3 (cos(π/6) + i sin(π/6))

then their product is

zw = 8•3 (cos(π/3 + π/6) + i sin(π/3 + π/6))

zw = 24 (cos(π/2) + i sin(π/2))

zw = 24i

The product of complex numbers z and w results in a point that is situated along the positive y-axis in the complex plane, being 24 units away from the origin.

In complex numbers, the geometric meaning of a product of two numbers, here zw, corresponds to the multiplication of the moduli and the addition of the arguments of the two numbers.

Here, z = 8(cos (pi/3) + i sin (pi/3)) and w = 3(cos(pi/6) + i sin (pi/6)), so the modulus of zw is 3*8 = 24.

The argument is the sum of the arguments (pi/3 + pi/6) which is pi/2. Hence, the product can be rewritten as zw = 24(cos(pi/2) + i sin(pi/2)). This geometric construction will situate the point along the positive y-axis in the complex plane, with a distance of 24 units from the origin.

Learn more about Complex Numbers here:

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