Question

8. The argument of the complex number 13-5i/4-9i is
a)[/3 b) 1/4 c)T/5 d) 1/6

Answer 1

The argument of the given complex number is π/4.

We have to find the argument of the complex number (13-5i)/(4-9i).

First of all, we have to solve the given complex number. we have to make it standard form of complex number.

Multiply and divide (4 + 9i) in  (13-5i)/(4-9i).

= (13-5i)/(4-9i) × ( 4 + 9i)/(4 + 9i)

= {(13 - 5i)(4 + 9i)}/{(4 - 9i)(4 + 9i)}

= {52 + 117i - 20i - 45i²}/{4² - 9²i²}

= (97 + 97i)/(16 + 81)

= (97 + 97i)/97

= 1 + i

Here, both real and imaginary parts of the complex number are positive so, argument lies in the first quadrant.

∴ argument = tan⁻¹ (b/a) = tan⁻¹(1/1) = π/4

Therefore the argument of the given complex number is π/4.