Задача 39784 Помогите со 2...

anzhela

2019-09-23 13:49:54

Помогите со 2

sova

2019-09-23 14:37:53

★

z=x+iy

|z|=sqrt(x^2+y^2)

z=1-4i

|z|=sqrt(1^2+(-4)^2)=sqrt(17)

[b]|z|^2=17[/b]

2.
i^2=-1
i^3=-i
i^4=1

i^32=(i^4)^8=1^8=1
i^29=i^(28)*i=(i^4)^7*i=1^7*i=i

[m]z=\frac{4i^{2}-5i^{32}}{-5-3i^{29}}=\frac{4\cdot (-1)-5\cdot 1}{-5-3i}=\frac{-9}{-5-3i}=\frac{9}{5+3i}[/m]

[m]\frac{9}{5+3i}=\frac{9\cdot (5-3i)}{(5+3i)(5-3i)}=\frac{9\cdot (5-3i)}{5^2-(3i)^2}=\frac{9\cdot (5-3i)}{25+9}=\frac{9\cdot (5-3i)}{34}[/m]

vector{z}=[m]\frac{9\cdot (5+3i)}{34}=\frac{45+27i}{34}=\frac{45}{34}+\frac{27}{34}i[/m]

Re vector{z}=[m]\frac{45}{34}=[/m]

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