Compute the following quantities: a) i^21-i^32
b) 2-i/3-2i.
show work

a) i-1; b) 4+i/13

Step-by-step explanation:

The complex number is defined as the number such that ;

We use the propperty to notice that .

a) We notice that . Hence, .

b) We multiply the expression by . Then we get that

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.