Classify the number 11-6i

a) real number
b) complex number
c) imaginary number

The number is B) complex number.

Here, let’s first see the type of numbers given in the options:

A) Real number:

The numbers which are used to denote the distance is real numbers. The numbers which come under real numbers is rational numbers and irrational numbers.

For example, -5, 2/3, , and so on.

B) Complex number:

The complex numbers are always written as:

Where ‘a’ and ‘b’ are real numbers and ‘i’ is imaginary number. Complex number is a set of all the numbers.

C) Imaginary number:

The numbers which doesn’t exist is imaginary number.

For example, the square is always positive, we cannot get a negative number as a square. So, the square root of the negative number becomes an imaginary number because that number doesn’t exist.

The imaginary number is denoted with ‘i’ where,

So, the given number is a complex number which has real number ‘11’ and imaginary number ‘6i’.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is