Using the general form of complex numbers a + bi, what are the values of a and b for the number i - 6?

a=-6; b=1

Explanation:

This is the same thing as saying -6+1i. Therefore for the general form a+bi, a equals -6 and b equals 1

a = -6 and b = 1

Step-by-step explanation:

We have given a complex number.

i-6

We have to find the value of a and b using general form of complex numbers.

The general form of complex numbers is a+bi.

given complex number can be written as:

-6+1i

Comparing with general form , we have

a = -6 and b = 1 which is the answer.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt