Question

Write the following quotient in the form a+bi.
-7i/2-7i

Answer 1

`\large\boxed{(49)/(53)-(14)/(53)i}`

Explanation:

`\text{Use}\\\\i=√(-1)\to i^2=-1\\\\(a-b)(a+b)=a^2-b^2\to(a-bi)(a+bi)=a^2+b^2\\\\\text{distributive property}\ a(b+c)=ab+ac\\---------------------\\\\(-7i)/(2-7i)=(-7i)/(2-7i)\cdot(2+7i)/(2+7i)=(-7i(2+7i))/(2^2+7^2)=((-7i)(2)+(-7i)(7i))/(4+49)\\\\=(-14i-49i^2)/(53)=(-14i-49(-1))/(53)=(-14i+49)/(53)\\\\=(49)/(53)-(14)/(53)i`

Answer 2

Write the following quotient in the form a+bi.

-7i/2-7i

Explanation: