Question

Simplify 3 over quantity of 5 minus 6 i

Answer 1

Answer:

Quantity of 15 plus 18 i over 61

Step-by-step explanation:

Here, the given expression,

3 over quantity of 5 minus 6 i

$\implies \frac{3}{5-6i}$

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,

$\frac{3}{5-6i}\times \frac{5+6i}{5+6i}$

$=\frac{3(5+6i)}{(5)^2-(6i)^2}$   ( (a+b)(a-b) = a² - b² )

$=\frac{15+18i}{25-36i^2}$

$=\frac{15+18i}{25+36}$   ( i² = -1 )

$=\frac{15+18i}{61}$

= 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.