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
[tex]\implies \frac{3}{5-6i}[/tex]
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,
[tex]\frac{3}{5-6i}\times \frac{5+6i}{5+6i}[/tex]
[tex]=\frac{3(5+6i)}{(5)^2-(6i)^2}[/tex] ( (a+b)(a-b) = a² - b² )
[tex]=\frac{15+18i}{25-36i^2}[/tex]
[tex]=\frac{15+18i}{25+36}[/tex] ( i² = -1 )
[tex]=\frac{15+18i}{61}[/tex]
= quantity of 15 plus 18 i over 61
First option is correct.
