ADD AND SUBTRACT COMPLEX NUMBERS

The number which is in the form of a + ib is known as complex number. Every complex numbers will have two parts. They are real part and imaginary part. 

To add and subtract complex numbers, we have to combine the real parts together and imaginary parts together.

(a + ib) + (c + id) : 

= (a + c) + (ib + id)

= (a + c) + i(c + d)

Example 1 :

Add (-3i) and (3 + 5i).

Solution :

(-3i) + (3 + 5i) = 3 + (-3i + 5i)

= 3 + 2i

Example 2 :

Add (-6 - 2i) and (6 - 5i).

Solution :

(-6 - 2i) + (6 - 5i) = (-6 + 6) + (-2i - 5i)

= 0 + (-7i)

= -3i

Example 3 :

Add (5 + 6i) and (2 - 7i).

Solution :

(5 + 6i) + (2 - 7i) = (5 + 2) + (6i - 7i)

= 7 + (-i)

= 7 - i

Example 4 :

Add (5 - 6i), 5i and (7 + 6i).

Solution :

(5 - 6i) + 5i + (7 + 6i) = (5 + 7) + (-6i + 5i + 6i)

= 12 + 5i

Example 5 :

Simplify :  (-7 + 7i) - (-7 - 3i) + (-7 - 8i).

Solution :

(-7 + 7i) - (-7 - 3i) + (-7 - 8i) = -7 + 7i  + 7 + 3i - 7 - 8i

= (-7 + 7 - 7) + (7i + 3i - 8i)

= -7 + 2i

Example 6 :

Simplify : (-4 - 7i) - (4 + 5i) - (2 - i).

Solution :

(-4 - 7i) - (4 + 5i) - (2 - i) = -4 - 7i - 4 - 5i - 2 + i

= (-4 - 4 - 2) + (-7i - 5i + i)

= -10 + (-11i)

= -10 - 11i

Example 7 :

Simplify : (1 + 6i) + (6 - 2i) - (-7 + 5i).

Solution :

(1 + 6i) + (6 - 2i) - (-7 + 5i) = 1 + 6i + 6 - 2i + 7 - 5i

(1 + 6 + 7) + (6i - 2i - 5i)

= 14 + (-i)

= 14 - i

Example 8 :

Simplify : (-5 + 7i) - (-6 + i) - (-6 + 5i).

Solution :

(-5 + 7i) - (-6 + i) - (-6 + 5i) = -5 + 7i + 6 - i + 6 - 5i

= (-5 + 6 + 6) + (7i - i - 5i)

= 7 + i

Example 9 :

Subtract (3 - 4i) from (8 + 2i).

Solution :

(8 + 2i) - (3 - 4i) = 8 + 2i - 3 + 4i

= (8 - 3) + (2i + 4i)

= 5 + 6i

Example 10 :

Subtract (-5 - i) from (2 - 7i).

Solution :

(2 - 7i) - (-5 - i) = 2 - 7i + 5 + i

= (2  + 5) + (-7i + i)

= 7 + (-6i)

= 7 - 6i

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