Question

Divide and express the resu (4i)/(5-i)

Answer 1

To divide (4i)/(5-i), multiply both the numerator and denominator by the conjugate of the denominator, resulting in 8i/13 after simplification.

Step-by-step explanation:

To divide the complex number (4i)/(5-i), we need to rationalize the denominator. This process involves multiplying the numerator and the denominator by the conjugate of the denominator. The conjugate of a complex number is the same as the original number, but with the sign of the imaginary part changed, so the conjugate of 5-i is 5+i.

Here are the steps to perform the division

1. Multiply the numerator and denominator by 5+i:
2. (4i)/(5-i) * (5+i)/(5+i) = (4i * (5+i)) / ((5-i) * (5+i))
3. Expand the numerator: 4i * 5 + 4i * i = 20i + 4i^2
4. Since i^2 = -1, we get 20i - 4 = 16i
5. Expand the denominator: 5^2 - i^2 = 25 - (-1) = 26
6. The division is now simplified to (16i)/26, which can be further simplified to 8i/13

The final answer is 8i/13.