Question

Divide 6/(3 + 5i), write the answer in standard form a + bi.

A. (9/17) - (15i/17)
B. (9/17) + (15i/17)
C. (9/34) - (15i/34)
D. (9/34) + (15i/34)

Answer 1

To divide 6/(3 + 5i) and write the answer in standard form a + bi, multiply the numerator and denominator by the conjugate of the denominator (3 - 5i) to eliminate the complex denominator. Finally, simplify and write the answer in standard form.

Therefore, the answer is A. (9/17) - (15i/17).

Step-by-step explanation:

To divide 6/(3 + 5i) and write the answer in standard form a + bi, we need to multiply the numerator and denominator by the conjugate of the denominator, which is 3 - 5i. This will eliminate the complex denominator.

Multiplying the numerator and denominator, we get:

(6/(3 + 5i)) * (3 - 5i)/(3 - 5i)

This simplifies to:

(18 - 30i)/(9 + 25)

Simplifying further, we have:

(18 - 30i)/34

Now, we can write the answer in standard form, a + bi:

(18/34) - (30i/34)

Therefore, the answer is A. (9/17) - (15i/17).