Question

Let z =38 (cos(pi/8)+ i sin(pi/8)) and w = 2 (cos( pi/16 ) + i sin(pi/16))

Answer 1

Answer:

$zw=76 * (cos(\frac{3\pi}{16}) +isin(\frac{3\pi}{16}) )$

Step-by-step explanation:

Given

$z =38 (cos(\frac{\pi}{8})+ i sin(\frac{\pi}{8})$ and

$w = 2 (cos(\frac{\pi}{16} ) + i sin(\frac{\pi}{16})$

Required

Determine zw

Given that:

$x = v_1(cos(a) + isin(a))$ and $y = v_2(cos(b) + isin(b))$

$x * y = (v_1 * v_2)*((cos(a+b) + isin(a+b))$

So, we have:

$zw=(38 * 2) * (cos(\frac{\pi}{8} + \frac{\pi}{16}) + isin(\frac{\pi}{8} + \frac{\pi}{16}))$

$zw=76 * (cos(\frac{2\pi + \pi}{16})+isin(\frac{2\pi + \pi}{16}))$

$zw=76 * (cos(\frac{3\pi}{16}) +isin(\frac{3\pi}{16}) )$