If a = –2 – 5i and b = –i, then find the value of the ab^3 in fully simplified form.

5 + 2i

We were given the complex numbers;

a = - 2 - 5i

and

b = - i

We want to find the product;

ab^3                            ^ = Exponent

We substitute the complex numbers into the expression and simplify

( - 2 - 5i ) (i)^3                     ^ = Exponent            

This is rewritten as:

( - 2 - 5i) (i)^2     x  i                           ^ = Exponent

Note that

i^2 = - 1                                            ^ = Exponent

We substitute to obtain:

( - 2 - 5i )  x  - i                

Let us expand to get:  

- 2 x - i + 5i  x  - i

This simplifies to:

2i - 5i^2                           ^ = Exponent

This gives:

2i - 5 ( - 1 ) = 2i + 5

Hope This Helps

DOH! My Brian Hurts

one of each metals

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet