Drag the tiles to the correct boxes to complete the pairs. Match each subtraction of complex numbers to its simplified difference.

Here are the complex numbers with their simplified differences

(7 -3i) - (6 - 4i) = 1 + i

(4 + 3i) - (6 +2i) = -2 - i

(4 + 5i) - (3 - 4i) = 1 + 9i

(5 + 4i) - (9 + i) = -4 + 3i

A complex number is when a real number and an imaginary number are added together

Complex numbers are usually in the form : a + bi

where a and b are real numbers and i is an imaginary number

for example, in this imaginary number : (7 -3i)

7 and 3 are real numbers while i is the imaginary number

In order to simplify these set of complex numbers, remember that when there is a bracket in mathematics it signifies multiplication.

Here are the set of rules that guide multiplication :

when a negative value is multiplied by a positive value, the value becomes a negative value

For example, -1 x 1 = -1

when a positive value is multiplied by a positive value, the value remains a positive value

For example, 1 x 1 = 1

when a negative value is multiplied by a negative value, the value becomes a negative value

For example,-1 x -1 = 1

Using the above information, the complex numbers can now be simplified

1. (7 -3i) - (6 - 4i)

this above equation becomes :

7 - 3i - 6 + 4i

add like terms together

7 - 6 - 3i + 4i  = 1 + i

2. (4 + 3i) - (6 +2i)

this above equation becomes :

4 + 3i - 6 - 2i

add like terms together

4 - 6 +3i - 2i = -2 - i

3. (4 + 5i) - (3 - 4i)

this above equation becomes :

4 + 5i - 3 + 4i

add like terms together

4 - 3 + 5i + 4i  = 1 + 9i

4. (5 + 4i) - (9 + i)

this above equation becomes :

5 + 4i -9 -i

add like terms together

5 -9 + 4i - i  = -4 + 3i

In order to solve for complex numbers remember that a bracket in mathematics means that a multiplication operation should be carried out. Also, pay cognisance to the rules guiding the multiplication of negative and positive numbers

Here is a similar question and answer on how to solve for complex numbers :

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.