does anyone know what (4 - 6i)/(4 + 6i) = ?
I do
ok, multiply top and bottom by (4-6i) to get
(4-6i)^2/(16-36i^2)
= 16 - 48i + 36i^2)/(16+36)
= (-20-48i)/52
= (-5 - 12i)/13
To find the value of the expression (4 - 6i)/(4 + 6i), we can simplify it using a technique called conjugate multiplication.
Step 1: Determine the conjugate of the denominator. To find the conjugate of a complex number, we need to change the sign of the imaginary part. In this case, the conjugate of (4 + 6i) is (4 - 6i).
Step 2: Multiply both the numerator and the denominator by the conjugate of the denominator. This process eliminates the imaginary part from the denominator.
So, (4 - 6i)/(4 + 6i) can be rewritten as:
[(4 - 6i) * (4 - 6i)] / [(4 + 6i) * (4 - 6i)]
Step 3: Simplify the expression.
Numerator:
(4 - 6i) * (4 - 6i) can be expanded using the FOIL method:
(16 - 24i - 24i + 36i^2)
Combining like terms and substituting i^2 = -1:
(16 - 48i + 36(-1))
(16 - 48i - 36)
(-20 - 48i)
Denominator:
(4 + 6i) * (4 - 6i) can also be expanded using the FOIL method:
(16 - 24i + 24i - 36i^2)
(16 - 36i^2)
Substituting i^2 = -1:
(16 - 36(-1))
(16 + 36)
(52)
So, [(4 - 6i) * (4 - 6i)] / [(4 + 6i) * (4 - 6i)] simplifies to (-20 - 48i) / 52 or -(5/13) - (12i/13).
Therefore, the expression (4 - 6i)/(4 + 6i) equals -(5/13) - (12i/13).