Find the modulus-argument form of the complex number z=(5√ 3 - 5i)

The easiest way to complete questions of these types is to first sketch an Argand diagram. With 5√ 3 on the x (real) axis and -5 on the y (imaginary) axis, the modulus would be calculated simply by using pythagoras's theorem. Thus, the modulus of z would be equal to √((5√3)² + 5²) = √(75+25) = √100 = 10. The argument is then found as the angle between the real axis and the vector of the complex number. This can once again be calculated with trigonometry. As we know the magnitude of all three edges of the triangle, any of sin cos and tan operations can be used. In this example, i will compute it using tan. thus, tan(θ)=opp/adj = Imimaginary/real components = -5/(5√3) therefore arg(z)=arctan(-1/√3), which gives a value of -30° or -π/6 once we have both the modulus and the argument of the complex number, expressing it in modulus-argument form is straightforward. the complex number z= |z|((cos(arg(z) + isin(arg(z))) = 10(cos(-π/6) + isin(-π/6) ).

CP
Answered by Chris P. Further Mathematics tutor

23739 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Two planes have eqns r.(3i – 4j + 2k) = 5 and r = λ (2i + j + 5k) + μ(i – j – 2k), where λ and μ are scalar parameters. Find the acute angle between the planes, giving your answer to the nearest degree.


Find the reflection of point P(2,4,-6) in the plane x-2y+z=6


Using graphs, show how the Taylor expansion can be used to approximate a trigonometric function.


A mass m=1kg, initially at rest and with x=10mm, is connected to a damper with stiffness k=24N/mm and damping constant c=0.2Ns/mm. Given that the differential equation of the system is given by d^2x/dt^2+(dx/dt *c/m)+kx/m=0, find the particular solution.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences