Question

How do you divide `( i+8) / (5i +5 )` in trigonometric form?

Answer 1

`C_3 = (40+5i-40i+5)/(25+25)= (45-35i)/50= 1/10(9-7i)`

Explanation:

Given the complex set `C_1 =( i+8)` and `C_2=(5i +5 )`
Required: `( i+8)/(5i +5 )`
Solution: Use complex conjugate of `C_2`, `bar(C_2)`to perform complex number division.
The product of a complex number `C` with it's conjugate `bar(C)` is: `R = C*bar(C) = (a+bi)(a-bi) =a^2+b^2`, a real number.
Thus multiplying top and bottom by `bar(C_2) = 5-5i`
`C_3 = (C_1*bar(C_2))/(C_2*bar(C_2)) = ((i+8)(5-5i))/((5+5i)*(5-5i))`

`C_3 = (40+5i-40i+5)/(25+25)= (45-35i)/50= 1/10(9-7i)`