Adding and Subtracting Imaginary and Complex Numbers

Write the expression in the form of a+bi, where a and b are real numbers.

3 ⋅ √-25

• 15

• -15

• 15i

• -15i

Simplify.

(-6 - 4i) + (1 + 4i) = _______

• -5

• -5+i

• -7-8i

• 5

Simplify.

(-5 - 5i) - (-3 + 6i)

Simplify.

(-10 + 4i) - (15 - 14i)

• -25+18i

• 25-18i

• 5-10i

• -5+10i

What is the result of adding Z1 and Z2, where Z1 = 3 + 2i and Z2 = -4 + i?

• -1 + 3i

• -1 - 3i

• 1 + 3i

• 1 - 3i

What is the resulting complex number when Z1 and Z2 are added as vectors?

• Z1 + Z2

• Z1 - Z2

• Z2 - Z1

• Z1 * Z2

What is the representation of the complex number 7 + i on an argand diagram?

• 7 units to the right, 1 unit up

• 7 units to the left, 1 unit down

• 7 units to the right, 1 unit down

• 7 units to the left, 1 unit up

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 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.

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.