Evaluate the expression√(-6)/(√(-3) √(-4)) and write the result in the form a+bi. Please help!!!!! :(
√(-6)/(√(-3) √(-4))
= (√6 i)/(√3 i * √4 i)
= (√6 i)/(2√3 i^2)
= (√3*√2 i)/(-2√3)
= -√2 i/2
= 0 - 1/√2 i
To evaluate the expression √(-6)/(√(-3) √(-4)) and write the result in the form a+bi, we need to simplify it step by step.
First, let's simplify the individual square roots:
√(-6) can be written as √(6) * i, where i represents the imaginary unit (√(-1)).
√(-3) can be written as √(3) * i.
√(-4) can be written as √(4) * i.
Now, let's substitute these values back into the original expression:
√(-6)/(√(-3) √(-4)) = (√(6) * i)/((√(3) * i) * (√(4) * i))
Next, let's simplify the denominator:
(√(3) * i) * (√(4) * i) = (√(3) * √(4)) * (i * i) = √(12) * i² = √(12) * (-1)
Remember that i * i = i², and by definition, i² = -1.
Now, let's substitute this back into the expression:
√(-6)/(√(-3) √(-4)) = (√(6) * i)/ (√(12) * (-1))
Next, let's simplify the numerator:
√(6) * i = √(6) * i
Now, let's substitute this back into the expression:
(√(6) * i)/ (√(12) * (-1)) = (√(6) * i)/(-√(12))
To simplify further, let's rationalize the denominator:
Multiply both the numerator and the denominator by (√(12)):
[ (√(6) * √(12) * i) ] / [ (-√(12) * √(12)) ]
Now, let's simplify:
[ (√(6) * √(12) * i) ] / [ -12 ]
[ √(6 * 12) * i ] / [ -12 ]
[ √(72) * i ] / [ -12 ]
[ √(36 * 2) * i ] / [ -12 ]
[ 6√(2) * i ] / [ -12 ]
[ 6√(2) * i ] / -12
Now, divide both the numerator and the denominator by 6:
[ √(2) * i ] / -2
So, the expression √(-6)/(√(-3) √(-4)) simplifies to (√(2) * i) / -2.
In the form a+bi, the result is:
-√(2)/2 * i