Which property of addition is shown below?
3 + 4i + 5 + 6i = 3 + 5 + 4i + 6i

Solution:

Given the equation

3 + 4i + 5 + 6i = 3 + 5 + 4i + 6i

By looking at the terms, we can say all are the same on either side of the equation and also give the same output.

According to the commutative property of addition property if we add two or more numbers we arrive at the same sum irrespective of their arrangement in any order.

The commutative property of addition is true for complex numbers.

If z\(_1\) = a + ib , z\(_2\) = c + id are the two complex numbers, then z\(_1\) + z\(_2\)= z\(_2\) + z\(_1\)

Here z\(_1\) = 3 + 4i and z\(_2\) = 5 + 6i

z\(_1\) + z\(_2\) = 3 + 4i + 5 + 6i

=(3 + 5) + i(4+ 6)

= 8 + 10 i

z\(_2\) + z\(_1\) = 5 + 6i + 3 + 4i

(5+3) + i(6+4)

= 8 + 10 i

Thus z\(_1\) + z\(_2\) = z\(_2\) + z\(_1\)

3 + 4i + 5 + 6i = 3 + 5 + 4i + 6i

Hence, the equation indicates the commutative property or the rearrangement property of the addition of complex numbers.