Add and Subtract Complex Numbers |

When performing the arithmetic operations of adding or subtracting on complex numbers, remember to combine "similar" terms. Also check to see if the answer must be expressed in simplest *a+ bi *form.

*Addition Rule:* (*a + bi*) + (*c + di*) = (*a + c*) + (*b + d*)*i* |

Add the "real" portions, and add the "imaginary" portions of the complex numbers.

Notice the distributive property at work when adding the imaginary portions.

*Additive Identity:* (*a + bi*) + (0 *+ *0*i*) = *a + bi* |

*Additive Inverse:* (*a + bi*) + (-*a - bi*) = (0* +*0*i*) |

ADD: (6 + 4*i*) + (8 - 2*i*)

Express answer in a + bi form.

(6 + 4*i*) + ( 8 - 2*i*) = 6 + 4*i *+ 8 - 2*i* = 6 + 8 + 4*i *- 2*i* = 14 + 2*i*

*Or by rule grouping: *(6 + 4*i*) + ( 8 - 2*i*) = (6 + 8) + (4 - 2)*i* = 14 + 2*i *

ADD: 3 + (-2 - 4*i*) + (5 + *i*) + (0 - 2*i*)

Express answer in a + bi form.

3 + (-2 - 4*i*) + (5 + *i*) + (0 - 2*i*) = 3 - 2 - 4*i *+ 5 + *i *- 2*i* = 6 - 5*i*

It is not necessary to always show the "grouping" of terms unless you are asked to do so.

ADD:

Express answer in a + bi form.

ADD:

Express answer in a + bi form.

*Subtraction Rule:* (*a + bi*) - (*c + di*) = (*a - c*) + (*b - d*)*i* |

Subtract the "real" portions, and subtract the "imaginary" portions of the complex numbers.

Notice the distributive property at work when subtracting the imaginary portions.
SUBTRACT: (10 + 3*i*) - (7 - 4*i*)

Express answer in a + bi form.

(10 + 3*i*) - (7 - 4*i*) = 10 + 3*i *- 7 - (-4*i*) = 10 - 7 + 3*i *+ 4*i *= 3 + 7*i*

*Or by rule grouping:* (10 + 3*i*) - (7 - 4*i*) = (10 - 7) + (3 - (-4))*i* = 3 + 7*i *

SUBTRACT:

Express answer in a + bi form.

SUBTRACT:

Express answer in a + bi form.