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Express in form a+in √3-2i/√3+2i​

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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

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