Question

What is the product of 3rad3cis(pi/8) and 3rad5cis(2pi/3)

Answer 1

Answer:

$9\sqrt{15}*cis(\dfrac{19\pi}{24})$

Step-by-step explanation:

To multiplying complex numbers in polar form, follow these steps:

• Multiply the polar magnitudes of the complex numbers.
• Add the angles of the complex numbers.

Given the two complex number in polar form

$3\sqrt{3}\:cis(\dfrac{\pi}{8})\:\:and\:\:3\sqrt{5}\:cis(\dfrac{2\pi}{3})\\\\3\sqrt{3}\:cis(\dfrac{\pi}{8})*3\sqrt{5}\:cis(\dfrac{2\pi}{3})=(3\sqrt{3}*3\sqrt{5})*cis(\dfrac{\pi}{8}+\dfrac{2\pi}{3})$

$=9\sqrt{15}*cis(\dfrac{3\pi+8*2\pi}{24})\\\\=9\sqrt{15}*cis(\dfrac{19\pi}{24})$