Question

Write the quotient in standard form. (Simplify your answer completely.)
2/6−5i 12/16 +10/61i

Answer 1

To simplify the expression and write the quotient in standard form, divide the numbers and subtract the exponents by multiplying the numerator and denominator by the conjugate of the second fraction.

Step-by-step explanation:

To simplify the expression and write the quotient in standard form, we need to first divide the numbers and then subtract the exponents. The given expression is:

(2/6 - 5i) / (12/16 + 10/61i)

To divide the numbers, we multiply the numerator and denominator of the first fraction by the conjugate of the second fraction:

(2/6 - 5i) * (16/12 - 61i/10)

Simplifying this expression, we get:

(32/72 - 320/120i - 305i/60 + 305/1000) / (192/192 + 61/10i - 732i/120 - 6572/1200)

Combining like terms and simplifying further, we get:

-529/1444 - 373/7278i

Therefore, the quotient in standard form is -529/1444 - 373/7278i.

Answer 2

To write the quotient of 2/6−5i divided by 12/16 +10/61i in standard form, you need to find the reciprocal of the divisor and then perform the multiplication. Finally, combine like terms and simplify the result to get the quotient in standard form.

Step-by-step explanation:

To write the quotient of 2/6−5i divided by 12/16 +10/61i in standard form, we need to perform the division and simplify the result completely.

1. First, we need to find the reciprocal of the divisor, which is 12/16 + 10/61i. The reciprocal of a complex number is found by flipping the numerator and denominator and changing the sign of the imaginary part. So, the reciprocal is 16/12 - 10/61i.
2. Next, we multiply the dividend 2/6−5i by the reciprocal 16/12 - 10/61i. To multiply complex numbers, we use the distributive property and multiply each term individually.
3. After performing the multiplication, we combine like terms and simplify the result to get the final quotient in standard form.

Once you perform the steps above, you will have the quotient of 2/6−5i divided by 12/16 +10/61i in standard form.