OPERATIONS WITH COMPLEX NUMBERS PRACTICE

Operations with Complex Numbers Practice :

In this section, we will see some example problems to show how to add, subtract, multiply and divide complex numbers.

Example 1 :

Add the following complex numbers

(2 + 3i) and (3 - 4i)

Solution :

To add two complex numbers which is in the form a + ib and c + id, we use the following method.

a + ib + c + id  =  (a + c) + i(b + d)

That is, we have to combine the real part and imaginary part separately.

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

  =  5 - i

Example 2 :

Add the following complex numbers

(4 - 5i) and (-2 + 3i)

Solution :

(4 - 5i) + (-2 + 3i)  =  (4 - 2) + (-5i + 3i)

  =  2 - 2i

Example 3 :

Add the following complex numbers

(-5 + 8i) + (9 - 11i)

Solution :

(-5 + 8i) + (9 - 11i)  =  (-5 + 9) + i(8 - 11)

  =  4 - 3i 

Example 4 :

Add the following complex numbers

(3 + 2i) and (-6 - 9i)

Solution :

(3 + 2i) + (-6 - 9i)  =  (3 - 6) + i(2 - 9)

  =  -3 - 7i

Example 5  :

Subtract

9 - 11i from 2 + 3i

Solution :

  =  (2 + 3i) - (9 - 11i)

  =  (2 - 9) + i(3 - 11)

  =  -7 - 8i

Example 6 :

Subtract

3 + 4i from 4 - 5i

Solution :

  =  (4 - 5i) - (3 + 4i)

  =  4 - 5i - 3 - 4i

  =  (4 - 3) - 5i - 4i

  =  1 - 9i

Example 7 :

Subtract

(-7 + 5i) from (-8 + 9i)

Solution :

  =  -8 + 9i - (-7 + 5i)

  =  -8 + 9i + 7 - 5i

  =  -8 + 7 + 9i - 5i

  =  -1 + 4i

Example 8 :

Subtract

(-11 - 13i) from (-8 - 9i)

Solution :

(-8 - 9i) - (-11 - 13i)  =  -8 - 9i + 11 + 13i

  =  (-8 + 11) + i(-9 + 13)

  =  3 + 4i

After having gone through the stuff given above, we hope that the students would have understood how to add and subtract complex numbers,

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