Chris Cruz

2022-01-17

Perform the indicated operation:
$7\left[\mathrm{cos}\left({228}^{\circ }\right)+i\mathrm{sin}\left({228}^{\circ }\right)\right]×8\left[\mathrm{cos}\left({232}^{\circ }\right)+i\mathrm{sin}\left({232}^{\circ }\right)\right]$

Cleveland Walters

Step 1
Topic - complex numbers
$56\left[\mathrm{cos}\left(460\right)+i\mathrm{sin}\left(460\right)\right]$
Multiplication of two complex numbers in polar coordinates: multiply the r components and add the $\theta$
Step 2
$7\left[\mathrm{cos}\left({228}^{\circ }\right)+i\mathrm{sin}\left({228}^{\circ }\right)\right]×8\left[\mathrm{cos}\left({232}^{\circ }\right)+i\mathrm{sin}\left({232}^{\circ }\right)\right]$
$=7×8\left[\mathrm{cos}\left({228}^{\circ }+232\right)+i\mathrm{sin}\left({228}^{\circ }+{232}^{\circ }\right)\right]$
$=56\left[\mathrm{cos}\left({460}^{\circ }\right)+i\mathrm{sin}\left({460}^{\circ }\right)\right]$
Answer: $56\left[\mathrm{cos}\left({460}^{\circ }\right)+i\mathrm{sin}\left({460}^{\circ }\right)\right]$

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