Add/Subtract/Multiply Complex Numbers

Match the following imaginary variables to their equivalent form.

• -1

True or False:

You must write complex numbers in the form a + bi, where the imaginary number comes last.

• True

• False

You can add and subtract like terms of complex numbers in the same way you add or subtract other like terms.

Try simplifying 4i+5i

• -1i

• 9i

• 20i

• 1i

Answer explanation

To simplify 4i + 5i, combine the coefficients of the like terms: 4 + 5 = 9. Thus, 4i + 5i = 9i. The correct answer is 9i.

4i+5i=9i

Just like 4+5=9 or 4x+5x=9x

Now let's try subtraction of imaginary terms

Simplify 4i - 5i

• -1i

• 9i

• 20i

• 1i

Answer explanation

To simplify 4i - 5i, subtract the coefficients: 4 - 5 = -1. Thus, 4i - 5i = -1i. The correct answer is -1i.

We're off to a good start learning about operations on imaginary numbers! Now let's try something complex (meaning a number with a real and imaginary part)

Identify the real part in this complex number

7+3i

• 7

• 3

• i

• 3i

Answer explanation

In the complex number 7+3i, the real part is the coefficient of the real component, which is 7. The imaginary part is represented by 3i, where 3 is the coefficient of the imaginary unit i.

Identify the imaginary part in this complex number

7+3i

• 7

• 3

• 3i

Answer explanation

In the complex number 7+3i, the imaginary part is represented by the coefficient of 'i'. Here, 3 is the coefficient, making the imaginary part 3i. Therefore, the correct answer is 3i.

Now that we've practiced identifying our real and imaginary parts, let's try adding complex numbers

What is the sum of 6+3i and 7+12i

• 18+10i

• 13+15i

• 15+13i

• 10+18i

Answer explanation

To add the complex numbers 6+3i and 7+12i, combine the real parts (6+7) and the imaginary parts (3i+12i). This gives 13 for the real part and 15i for the imaginary part, resulting in 13+15i, which is the correct answer.

Last one, let's make it a subtraction problem

What is the simplifies form of

(11 - 7i) - (-3 + 12i)

(remember to distribute the negative)

• 8 - 19i

• 8 + 5i

• 13- 19i

• 14 -19i

Answer explanation

To simplify (11 - 7i) - (-3 + 12i), distribute the negative: (11 - 7i) + (3 - 12i). Combine real parts: 11 + 3 = 14, and imaginary parts: -7 - 12 = -19i. Thus, the result is 14 - 19i.