Find the modulus and argument of this complex numbers 5+i/2+3i

(5+i)/(2+3i)

= (5+i)/(2+3i) * (2-3i)/(2-3i) = 1-i
Now finish it off

Did you know?

Did you know that the modulus and argument can be found for complex numbers? For example, let's consider the complex number (5 + i) divided by (2 + 3i). The modulus of a complex number represents its distance from the origin on the complex plane, which can be found by taking the square root of the sum of the squares of its real and imaginary parts. In this case, the modulus would be √[(5^2 + 1^2)/(2^2 + 3^2)] ≈ √(26/13) ≈ √2. The argument of a complex number refers to the angle it forms with the positive real axis on the complex plane and can be found by taking the inverse tangent of the quotient of the imaginary part over the real part. In this case, the argument would be atan(1/5) ≈ 0.1974 radians. By calculating the modulus and argument, we can better understand the properties and geometric representation of complex numbers.