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.
How to Add Subtract Multiply and Divide Complex Numbers ?
Addition and subtraction of complex numbers :
Suppose a, b, c, and d are real numbers. Then
- (a + bi) + (c + di) = (a + c) + (b + d)i
- (a + bi) − (c + di) = (a − c) + (b − d)i
Multiplying complex numbers :
Suppose a, b, c, and d are real numbers. Then,
- (a + bi)(c + di) = (ac − bd) + (ad + bc)i
Division of complex numbers :
Suppose a, b, c, and d are real numbers, with c + di ≠ 0. Then (a + bi)/(c + di)
= [(ac + bd) / (c2 + d2)] + [(bc − ad)(c2 + d2) i]
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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