Question

Multiply.

$\frac{\sqrt{2}}{6}cis (\frac{3\pi }{5})$·$\frac{\sqrt{6}}{4}cis (\frac{2\pi }{3})$

A.$\frac{\sqrt{3}}{12}cis(\frac{19\pi }{15})$
B. $\frac{\sqrt{3}}{12}cis(\frac{2\pi }{5})$
C. $\frac{\sqrt{2}}{8}cis(\frac{2\pi }{5})$
D. $\frac{\sqrt{2}}{8}cis(\frac{19\pi }{15})$

Answer 1

Multiply the moduli and add the arguments:

√2/6 cis(3π/5) × √6/4 cis(2π/3)

= (√2/6 × √6/4) cis(3π/5 + 2π/3)

= √3/12 cis(19π/15) … [A]