Question

Divide.
a.1 − 2i/2i
b. 5 − 2i/5 + 2i
c.√3 − 2i/−2 − √3i

Answer 1

(a) \frac{-1i}{2}-1[/tex]

(b)
`(20i+21)/(29)`

(c) i

Explanation:

We have to perform division

(a)
`(1-2i)/(2i)`

So after division

`(1-2i)/(2i)=(1)/(2i)-(2i)/(2i)=(-1i)/(2)-1`

(b) We have given expression
`(5-2i)/(5+2i)`

After rationalizing
`(5-2i)/(5+2i)* (5-2i)/(5-2i)=((5-2i)^2)/(25+4)=(25+4i^2+20i)/(29)=(20i+21)/(29)`

(c) We have given expression
`(√(3)-2i)/(-2-√(3i))`

After rationalizing

`(√(3)-2i)/(-2-√(3i))* (-2+√(3i))/(-2+√(3i))=(-2√(3)+7i+2√(3))/(7)=(7i)/(7)=i`