(5-4i)/(8+i) ~ simplify the expression
(i=imaginary #)
help plz! thanks!
Multiply numerator and denominator by 8-i to make the denominator real.
(5-4i)(8-i)/[8+i)(8-i)] = [40-37i-4]/65
= (36-37i)/65
(5-4i)(8+i)=40+5i-40i-4i*i(4 square) =40-35i-4i*i
Rita: The question did not ask for a multiplication. It was a division. Your multiplication also contains an error.
what makes 425 in times tables
To simplify the expression (5-4i)/(8+i), you need to first get rid of the complex number in the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.
The conjugate of a complex number a+bi is obtained by changing the sign of the imaginary part, so the conjugate of 8+i is 8-i.
Next, multiply the numerator and denominator by the conjugate 8-i:
((5-4i)/(8+i)) * ((8-i)/(8-i))
To multiply complex numbers, you can use the distributive property.
Now, multiply the numerators together and the denominators together:
((5-4i)(8-i))/((8+i)(8-i))
To simplify this expression, you distribute the terms in the numerator and denominator:
(40 - 5i - 32i + 4i²)/(64 - 8i + 8i - i²)
Remember that i² is equal to -1, so you can substitute the value:
(40 - 5i - 32i + 4(-1))/(64 - 8i + 8i - (-1))
Simplifying further:
(40 - 5i - 32i - 4)/(64 - 8i + 8i + 1)
Combine like terms:
(36 - 37i)/(65)
Therefore, the simplified expression is:
(36 - 37i)/65