ADD AND SUBTRACT COMPLEX NUMBERS

About "Add and subtract complex numbers"

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.

(1) Real part

(2) Imaginary part

Th number which is without the variable (i) is known as real part. The number which is with the variable (i) is known as imaginary part.

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

Let us see some example problems to understand the above concept.

Example 1 :

Add (−3i) and (3 + 5i)

Solution :

The first complex contains only imaginary part, but the second complex is having both real and imaginary parts.

Since there is no real part in the first complex number, we have to consider the real part as 0.

=  (−3i) + (3 + 5i)

=  (0 + 3i) + (3 + 5i)

Combining the real and imaginary parts together

=  (0 + 3) + (3i + 5i)

=  3 + 8i

Hence the answer is 3 + 8i

Example 2 :

Add (−6 − 2i) and (6 − 5i) 

Solution :

=  (−6 − 2i) + (6 − 5i) 

=  (-6 + 6) + (-2i - 5i)

=  0 - 7i

Hence the answer is 7i.

Example 3 :

Add (5 + 6i) + (2 − 7i)

Solution :

=  (5 + 6i) + (2 − 7i)

=  (5 + 2) + (6i - 7i)

=  7 - i

Hence the answer is 7 - i.

Example 4 :

Add (5 − 6i), 5i and (7 + 6i)

Solution :

=  (5 − 6i) + (5i) + (7 + 6i) 

=  (5 + 7) + (-6i + 5i + 6i)

=  12 + 5i

Hence the answer is 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 )+ i(7 + 3 - 8)

=  -7 + i(10 - 8)

=  -7 + 2i

Hence the answer is -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)+ i(-7 - 5 + 1)

=  -10 + i(-12 + 1)

=  -10 - 11 i

Hence the answer is -10 - 11 i

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)+ i(6 - 2 - 5)

=  14 + i(6 - 7)

=  14 - 1 i

Hence the answer is 14 - 1 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)+ i(7 - 1 - 5)

=  (12 - 5) + i(7 - 6)

=  7 +  i

Hence the answer is 7 + 1 i

After having gone through the stuff given above, we hope that the students would have understood "Add and subtract complex numbers". 

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