Question

Simplify 3 over quantity of 5 minus 6 i

quantity of 15 plus 18 i over 61

quantity of negative 15 plus 18 i over 61

3 i over quantity of 6 plus 5 i

quantity of 15 plus 18 i over negative 11

Answer 1

Quantity of 15 plus 18 i over 61

Explanation:

Here, the given expression,

3 over quantity of 5 minus 6 i

`\implies (3)/(5-6i)`

To simplify this we need to multiply the numerator and the denominator by the complex conjugate of the denominator,

Since, denominator = 5-6i,

Its conjugate = 5 + 6i

Multiply and divide above fraction by 5 + 6i,

`(3)/(5-6i)* (5+6i)/(5+6i)`

`=(3(5+6i))/((5)^2-(6i)^2)` ( (a+b)(a-b) = a² - b² )

`=(15+18i)/(25-36i^2)`

`=(15+18i)/(25+36)` ( i² = -1 )

`=(15+18i)/(61)`

= quantity of 15 plus 18 i over 61

First option is correct.

Answer 2

To simplify, we write the statement as an expression. We write it as follows:

3 over quantity of 5 minus 6 i
3/(5-6i)

The correct answer from the choices listed above would be the last option. The answer would be quantity of 15 plus 18 i over negative 11. Hope this answers the question. Have a nice day.