Question

Write
5 + 3i divided by 2 (2 + i) in the form a + bi, where a, b  R.

what am i supossed to do?

Answer 1

\[5+3i \div 4+2i] so then youmove the 3i to the other side by subrtacting [5\div4+i] then you move the 5 in the same way and you get -1+i\]

Answer 2

thanx

Answer 3

i'm not sure if that's right, so you might want to double check...

Answer 4

okay

Answer 5

\[\frac{5+3i}{2(2+i)}\]
multiply numerator and denominator by the conjugate of teh denominator. since the denominator is 2+i, the conjugate is 2-i so multiply numerator and denominator with that
\[\implies \frac{5+3i}{2(2+i)} \times \frac{2-i}{2-i}\]
\[\implies \frac{(5+3i)(2-i)}{2(2+i)(2-i)}\]
simplify by FOILing
\[\implies \frac{10 -5i + 6i - 3i^2}{2(4 - i^2)}\]
combine like terms
\[\implies \frac{10 + i - 3i^2}{2(4-i^2)}\]
transform i^2 into -1
\[\implies \frac{10 + i - 3(-1)}{2(4 - (-1))}\]
simplify
\[\implies \frac{10 + i + 3}{2(4+1)}\]
combine like terms
\[\implies \frac{13+i}{2(5)}\]
simplify the denominator
\[\implies \frac{13+i}{10}\]
did you get it?