Example for complex conjugates

In grade 10 math , complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of opposite signs. For example, 3 + 4i and 3 - 4i are complex conjugates.
The conjugate of the complex number z

where a and b are real numbers, is

An alternate notation for the complex conjugate is z * . However, the notation avoids confusion with the notation for the conjugate transpose of a matrix, which can be thought of as a generalization of complex conjugation. If a complex number is represented as a 2×2 matrix, the notations are identical.We also can use scientific notation converter to find the number.

Let's an example problem from numeric and algebraic operations


Question:-

How do you use complex conjugates to find (3+7i)/(2-i) ?


Answer:-


In the Given problem the denominator is (2-i)

So ,it's conjugate is (2+i)

Multiplying both numerator and denominator with (2+i)

= (3+7i)(2+i)/(2-i)(2+i)

= (5+17i)/(4-i²)

We know that i² = -1

= (5+17i)/4+1

= (5+17i)/5 Answer