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Evaluate the expression

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3 Answers

(-1 - 2i)/(8i)
 
Multiply by i/i
 
(-i + 2)/(-8)
 
(-2 + i)/8
 
-1/4 + 1/8 i
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
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 iis really -1, you get -8i - (-16) which is -8i +16, or in a + bi format, 16 -8i. 
 
On the bottom you get 64iand again, since iis -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