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

What is the product of zw?

Question

Let z =38 (cos(pi/8)+ i sin(pi/8)) and w = 2 (cos( pi/16 ) + i sin(pi/16))   What is the product of zw?

Philomena · Answer

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}) )

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