Evaluate the expression

Question

Evaluate the expression (-1-2i)/(8i) and write the results in the form a+bi

the real number a equals=

the real number b equals=

 

Answer 1

(-1 - 2i)/(8i)

 

Multiply by i/i

 

(-i + 2)/(-8)

 

(-2 + i)/8

 

-1/4 + 1/8 i

Answer 2

Hi Dalia,

 

(-1-2i)/8i=(-1-2i)/(0+8i)

 

multiply the numerator and denominator by (0-8i)

 

          =(-1-2i)(0-8i)/(0+8i)(0-8i)

 

          =(-1-2i)(-8i)/(8i)(-8i)

 

          =(8i+16i²)/-64i²   (i²=-1)

 

          =(8i-16)/64

 

          =8i/64-16/64

 

          =-16/64+8i/64

 

         =-1/4+i/8

 

a+bi=-1/4+i/8

 

a=-1/4  and  b=1/8

Answer 3

When you are dividing, you can not have an imaginary number in the denominator (bottom of the fraction), just like you cannot have a radical in the denominator. To get rid of it, you multiply both the top and the bottom by 8i so you will get:

 

{(-1 - 2i)(8i)}/{(8i)(8i)}

 

On the top you must distribute the 8i so you get -8i -16i². Since i² is really -1, you get -8i - (-16) which is -8i +16, or in a + bi format, 16 -8i. 

 

On the bottom you get 64i² and again, since i² is -1, you get -64. 

 

This leaves you with (16 -8i)/-64.

Since all of these terms have a common factor, we can factor out a -8. When we do this we get:

 

(-2 + i)/8

 

in a + bi format this would be -2/8 + i/8 where the first fraction can again be reduced to -1/4.

 

This would mean a = -1/4 and b= 1/8