Question

Simplify the following Complex Numbers.

\frac{1-3i}{2+5i}
2+5i
1−3i
​

Answer 1

`(-13 - 11i)/(29)`

Explanation:

You need to multiply the numerator and denominator by the conjugate of

2 + 5i, which is 2 - 5i

So,
`((1 - 3i)(2 - 5i))/((2 + 5i)(2 - 5i)) = (2 - 11i - 15)/(4 +25) = (-13 - 11i)/(29)`

Answer 2

{1-3i}{2+5i}

Explanation:

1. 1(2+5i)-3i(2+5i)
2. 2+5i-6i+15i2
3. 2+5i-6i+15(-1)
4. 2+5i-6i-15
5. 2-15+5i-6i
6. -13-i (answer)