Express the following expression in the form of a + ib.
\(\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}\)
Express the following expression in the form of a + ib.
\(\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}\)
Solution and Explanation
\(\dfrac{(3+i√5)(3-i√5)}{(√3+√2i)-(√3-i√2)}\)
\(=\dfrac{(3^2+(i√5)^2)}{√3+√2i-√3+i√2}\)
\(=\dfrac{9-5i^2}{(2√2i)}\)
\(=\dfrac{9+5}{(2√2i)}×\dfrac{i}{i}\)
\(=\dfrac{14i}{2√2i^2}\)
\(=\dfrac{-7i}{√2}\)
\(=\dfrac{-7i}{√2}×\dfrac{√2}{√2}\)
\(=\dfrac{-7√2i}{2}\) (Ans)
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
