Simplifying Imaginary Numbers and Adding/Subtracting Complex Numbers

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.

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.

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.

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