Complex numbers subtraction is explained

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Consider two complex numbers `z_1=a_1+ib_1` and `z_2 = a_2+ib_2`. What is `z_1-z_2`?

- `(a_1-a_2) + i (b_1-b_2)`
- `(a_1-a_2) + i (b_1-b_2)`
- `a_1-ib_1`
- `a_2-ib_2`

The answer is '`(a_1-a_2) + i (b_1-b_2)`'. This is from the associative and distributive laws of real numbers extended to numbers with `sqrt(-1)`.

Complex number Subtraction:

`z_1-z_2`

`quad quad =a_1+ib_1 - (a_2+ib2)`

`quad quad =a_1-a_2+ib_1-i_b2` (associative law)

`quad quad = a_1-a_2+ i(b_1-b2)` (distributive law)

`quad quad =`(a_1-a_2) + i (b_1-b_2) (real and imaginary parts of result)`

Subtraction of two complex numbers is the subtraction of real and imaginary parts individually.

**Subtraction of Complex numbers : **For any complex number `z_1=a_1+ib_1 in CC` and `z_2 = a_2+ib_2 in CC`

`z_1-z_2 = (a_1-a_2)+i(b_1-b_2)`

*Solved Exercise Problem: *

Given `z_1 = 2.1+i` and `z_2 = -2.1+i` What is `z_1-z_2`?

- `4.2+2i`
- `4.2`
- `4.2`
- `4.2-2i`
- `-4.2+2i`

The answer is '`4.2`'

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