Help me ! Solve problems working with imaginary numbers

1) 8 + 2i

2) -13

3) 15 + 3i

4) 1

5) 24 - 10i

Step-by-step explanation:

Working with imaginary numbers is similar to working with a variable when it comes to addition and subtraction, so for problems 1 and 3, it is a matter of combining like terms.

1) The like terms are 7i and -5i; 5 and 3. We can combine them.

8 + 2i

2) We can start to compute the problem by noticing it is a special product of difference of squares. The expression can also be written as:

(3i)^2 - (2)^2

9i^2 - 4

i is defined as the square root of negative 1, so i^2 is -1. We can substitute that in:

9(-1) - 4

-9 - 4

-13

3) We can combine the like terms, 12i and -9i; 5 and 10:

15 + 3i

4)The powers of i repeat every four numbers. For example:

i^1 = i

i^2 = -1

i^3 = -i

i^4 = 1

i raised to a power divisible by four is always 1, so i^24 is 1.

5) We can start by normally distributing in this problem:

12 - 18i + 8i - 12i^2

As said before, i^2 is -1:

12 - 10i + 12

24 - 10i

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐