Performing Arithmetic with Complex Numbers

a

When adding and subtracting complex numbers, we add and subtract the real parts and imaginary parts separately.

(2 + 3 i) + (4 + 2 i)

RemoveParRemove parentheses

2 + 3 i + 4 + 2 i

AddTermsAdd terms

6 + 5 i

The numbers add up to

6 + 5 i .

b

Proceed in the same way as in the previous sub-exercise.

(6 - 2 i) + (9 i - 2)

RemoveParRemove parentheses

6 - 2 i + 9 i - 2

AddSubTermsAdd and subtract terms

4 + 7 i

The result of the addition is, therefore,

4 + 7 i .

c

This time, we are going to subtract two complex numbers. This is done in a similar fashion as before. The only difference is that we have to flip the signs when removing the parentheses around the second term.

(3 + 10 i) - (3 - 12 i)

RemoveParRemove parentheses

3 + 10 i - (3 - 12 i)

RemoveParSignsRemove parentheses and change signs

3 + 10 i - 3 + 12 i

AddSubTermsAdd and subtract terms

22 i

The subtraction results in

22 i .

d

Let's now do the same thing once more.

- (20 i - 3) - (4 - 8 i)

RemoveParSignsRemove parentheses and change signs

- 20 i + 3 - 4 + 8 i

AddSubTermsAdd and subtract terms

- 1 - 12 i

The result is

- 1 - 12 i .

Performing Arithmetic with Complex Numbers 1.21 - Solution