Find the modulus and argument of the complex number 1+2i

It is always helpful to start by drawing a diagram with a Real and Imaginary axis then plotting the number (in our case 1+2i) on the diagram and drawing a line from the origin to our point. Remember the modulus tells us the distance between our point and the origin, and the argument gives us the angle between our number and the positive real axis. To find the modulus, which we will call r, we can use Pythagoras theorem: a^2 + b^2 = c^2. So, we can see that r^2 = 1^2 + 2^2 and therefore r= sqrt(2). To find the argument we want to find the angle theta from the real axis to our point, so we need to use SOH CAH TOA. Since we know the length of the Opposite side and the Adjacent side, we can use that tan(theta) = Opposite/Adjacent. Just use the inverse of tan to obtain theta. i.e. theta = arctan(Opposite/Adjacent),

Related Further Mathematics A Level answers

All answers ▸

Find the general solution for the determinant of a 3x3 martix. When does the inverse of this matrix not exist?


Given that y = arcsinh(x), show that y=ln(x+ sqrt(x^2 + 1) )


Prove by induction that 2^(6n)+3^(2n-2) is divsible by 5. (AS Further pure)


A particle is undergoing circular motion in a horizontal circle, that lies within the smooth surface of a hemispherical bowl of radius 4r. Find the distance OC (explained in diagram) if the angular acceleration of the particle is equal to root (3g/8r).


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences