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=

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

Multiply by i/i

(-i + 2)/(-8)

(-2 + i)/8

-1/4 + 1/8 i

Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...

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

Rachel W. | Hispanic Studies Major, Mathematics MinorHispanic Studies Major, Mathematics Mino...

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 -16i^{2}. Since i^{2 }is really -1, you get -8i - (-16) which is -8i +16, or in a + bi format, 16 -8i.

On the bottom you get 64i^{2 }and again, since i^{2 }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

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