Asked by Anonymous
What is the rectangular form(a + bi) of:
1. 5 cis(255°)
2. sqrt3 cis (11pi/6)
1. 5 cis(255°)
2. sqrt3 cis (11pi/6)
Answers
Answered by
Reiny
5 cis(255°)
= 5(cos255° + i sin255) , note that 225 is (180 + 45)° , quadrant III
thus cos 225 = -cos45 = -√2/2
and sin 225 = -sin45 = -√2/2
5cis225
= 5(-√2/2 - √2/2 i)
= -5√2/2 - 5√2/2 i
for the second, 11π/6 is a multiple of π/6 , (or 30°)
so follow my procedure
= 5(cos255° + i sin255) , note that 225 is (180 + 45)° , quadrant III
thus cos 225 = -cos45 = -√2/2
and sin 225 = -sin45 = -√2/2
5cis225
= 5(-√2/2 - √2/2 i)
= -5√2/2 - 5√2/2 i
for the second, 11π/6 is a multiple of π/6 , (or 30°)
so follow my procedure
Answered by
Steve
hmmm. is 255 a typo for 225? Probably.