2006-11-27 06:46:39 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The key is that with division, you need to multiply the top and bottom by the conjugate of the denominator. The conjugate is like this:
The conjugate of a+bi is
a-bi.
In this case, the denominator is 10+i. The conjugate will be 10-i.
(7+6i)/(10+i)=
Multiply by the conjugate
((7+6i)(10-i))/((10+i)(10-i))=
Simplify, but remember that -i*i = -(-1) = 1. So if you have an i and -i, the result will be positive. (treat i like a variable-use foil to expand)
(70+53i+6)/(100+1)=
Simplify
(76+53i)/101
Your real part will be 76/101, your imaginary part will be 53(i)/101
2006-11-27 06:51:09 · answer #1 · answered by Aegor R 4 · 2⤊ 0⤋
(7 + 6i) / (10 + i)
Multiply by (10 - i) / (10 - i).
= (70 - 7i + 60i + 6) / (100 + 1)
= (76 + 53i) / 101
= 76/101 + (53/101)*i
2006-11-27 06:55:54 · answer #2 · answered by falzoon 7 · 1⤊ 0⤋
(7 + (6 * i)) / (10 + i) = 0.752475248 + 0.524752475 i
2006-11-27 06:49:36 · answer #3 · answered by DanE 7 · 0⤊ 1⤋