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Гар77
@Гар77
July 2022
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Тригонометрическая форма комплексного числа z=3-3i имеет вид ?
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ludmilagena
Verified answer
Z=a+bi
z=3-3i
a=3; b=-3; a =r*cos fi; b = r*sin fi
r=| z| =√(a²+b²)=√(9+9)= √18=3√2
cos fi =a/r=3/(3√2)=1/√2
sin fi=b/r= - 3/(3√2)= - 1/√2
fi = -π/4
z=3√2 *(cos(-π/4) +i*sin(-π/4) )
z=3√2*(cosπ/4 - i*sinπ/4)
ответ: z=3√2*(cosπ/4 - i*sinπ/4)
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Answers & Comments
Verified answer
Z=a+biz=3-3i
a=3; b=-3; a =r*cos fi; b = r*sin fi
r=| z| =√(a²+b²)=√(9+9)= √18=3√2
cos fi =a/r=3/(3√2)=1/√2
sin fi=b/r= - 3/(3√2)= - 1/√2
fi = -π/4
z=3√2 *(cos(-π/4) +i*sin(-π/4) )
z=3√2*(cosπ/4 - i*sinπ/4)
ответ: z=3√2*(cosπ/4 - i*sinπ/4)