Question

Write the quotient135 - iin the form a bi0 A 135号-1B5 - 131C. 5+íD6524

Answer 1

The question is given as;

`(13)/(5-i)`

To write in form of a+bi , is the standard form of complex numbers.In this case,

you are performing division given a complex number

You find the conjugate of the denominator 5-i which is 5 + i

Then multiply the numerator and denominator with the conjugate as;

`(13(5+i))/((5-i)(5+i))`

This will give;

`(65+13i)/(5(5+i)-i(5+i))`

Note that

`i^2\text{ = -1}`

so this will be

`(65+13i)/(25+5i-5i-1i^2)=(65+13i)/(25-1)=(65)/(24)+(13i)/(24)`

The correct answer choice is D.