(Complex Numbers) Find each quotient: 8i/(2+2i)

Question

hartnn · Answer

can you find the conjugate of 2+2i first ?

hartnn · Answer

because you'll need to multiply the numerator and denominator by the conjugate of 2+2i

anonymous · Answer

Yeah it's (2-2i), I multiplied the numerator and denominator by it and my end result was: (16+16i)/8, but the answer key in the textbook says it's suppose to be: 2+2i. That's why I know something's not right. Is it just simplified that way because of the 16/8=2?

hartnn · Answer

yes, thats correct. 
when you factor out 8 from the numerator, you get 
8(2+2i)/8 = just 2+2i :)

nurali · Answer

$$\frac{ 8i }{ 2+2i }$$

Multiply and Divided by 2-2i

$$\frac{ 8i(2-2i) }{ (2+2i)(2-2i) }$$

$$\frac{ 16i-16i^2 }{ 4-4i+4i-4i^2 }$$

$$i^2=-1$$

$$\frac{16i+16 }{ 8 }$$

Taking Common

$$\frac{ 8(2+2i) }{ 8 }$$

$$2+2i$$

anonymous · Answer

Yeah I see it. Thank you!

nurali · Answer

My Pleasure.