Question

Divide (6 - i) / (-5 - 2i), write the answer in standard form a + bi.

A) -32/29 + 7/29 i
B) -32/29 - 7/29 i
C) -32/21 + 7/21 i
D) -32/21 - 7/21 i

Answer 1

To divide (6 - i) / (-5 - 2i) and write the answer in standard form a + bi, multiply the numerator and denominator by the conjugate of the denominator to eliminate the imaginary terms. Simplify the expression to get -32/29 + 7/29i.

Step-by-step explanation:

To divide (6 - i) / (-5 - 2i) and write the answer in standard form a + bi, we can use the distributive property to simplify the expression. First, multiply the numerator and denominator by the conjugate of the denominator, which is (-5 + 2i). This will eliminate the imaginary terms in the denominator.

Multiplying (6 - i) / (-5 - 2i) by (-5 + 2i) / (-5 + 2i) gives us [(6 - i)(-5 + 2i)] / [(-5 - 2i)(-5 + 2i)].

Simplifying further, the expression becomes [-32 + 7i] / [29].

Writing the answer in standard form a + bi, we have -32/29 + 7/29i.