Question

Divide and express the result in stand (7i)/(4-5i)

Answer 1

To divide (7i)/(4-5i) and express it in standard form, multiply numerator and denominator by the conjugate of the denominator, simplify, and separate the real and imaginary parts. The final standard form is -35/41 + 28i/41.

Step-by-step explanation:

To divide and express the result in standard form for the complex number (7i)/(4-5i), one should apply the concept of conjugate pairs. The strategy involves multiplying both the numerator and the denominator by the conjugate of the denominator, which, in this case, is (4+5i). Multiplying by the conjugate simplifies the denominator to a real number, which allows for a standard form representation. Here's the step-by-step calculation:

• 
  Multiply both numerator and denominator by the conjugate of the denominator:

(7i) / (4-5i) * (4+5i) / (4+5i)

• Apply the distributive property in the numerator and the denominator separately:

(7i*4 + 7i*5i) / (4*4 - 5i*5i)

• Simplify both parts:

(28i + 35i²) / (16 - 25i²)

• Since i² = -1, substitute and simplify further:

(28i + 35(-1)) / (16 - 25(-1))

• Conclude the simplification:

(28i - 35) / (16 + 25)

• Combine like terms:

(-35 + 28i) / 41

• Separate the real and imaginary parts:

-35/41 + (28/41)i

The final answer is -35/41 + 28i/41, which is the complex number in standard form.