To express (√3 - 2i)/(√3 + 2i) in the form a + bi, multiply both the numerator and denominator by the conjugate of the denominator and simplify, resulting in the complex number (-1/7) - (4√3/7)i.
To express the complex number (√3 - 2i)/(√3 + 2i) in the form a + bi, we use the method of rationalizing the denominator.
This involves multiplying both the numerator and the denominator of the fraction by the conjugate of the denominator.
The conjugate of √3 + 2i is √3 - 2i.
First, multiply the numerator and denominator:
(√3 - 2i) * (√3 - 2i) / (√3 + 2i) * (√3 - 2i)
Expand and simplify:
((3 - 4i√3 + 4i²)) / (3 - 4i√3 - 4i²)
Since i² = -1, simplify further:
((3 - 4i√3 - 4)) / (3 - 4i√3 + 4)
Simplify the real parts and the imaginary parts separately:
(-1 - 4i√3) / (7)
This gives us:
(-1/7) - (4√3/7)i