How do you multiply #e^((19 pi )/ 12 ) * e^( pi/4 i ) # in trigonometric form?

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Answer 1 · 2018-05-01T04:35:59

# e^{{19 pi}/12 i } e^{ pi/4 i} ## = e^{i ({19 pi}/12 + pi/4) } # # = e^{i (-pi/6 )} # # = \sqrt{3}/2 - i/2 #

I'm betting both of those are meant to have a factor of #i#.

# e^{{19 pi}/12 i } e^{ pi/4 i} #

# = e^{i ({19 pi}/12 + pi/4) } #

# = e^{i ({19 pi}/12 + {3pi}/12) } #

# = e^{i ({22 pi}/12 ) } #

# = e^{i ({11 pi}/6 ) } #

# = e^{i (-pi/6 )} #

# = cos (pi/6) - i sin (pi/6) #

# = \sqrt{3}/2 - i/2 #