Complex Numbers

Importance

Complex numbers have consequential significance in Mathametics.Since, problems can be expressed geometrically in which x-axis is represented by real number line and y-axis by the complex line, calculations can be reduced to great extent. We will give a flash on this topic on the basis of questions asked from this section.

Yearly trend

It can be clearly seen that a lot of questions are asked in JEE-Advanced and especially JEE-Mains and carry lot of weightage.Observing the characteristics of questions asked in previous year examinations, undermentioned topics are must for scoring cent.

Topics

Cartesian Representation

A complex number z can be represented of the form a+ib, where a is the real part and b is the imaginary part and !!i=sqrt(-1)!!. Here, !!|z|=sqrt(a^2+b^2)!! and its conjugate !!barz=a-ib!!.

Polar Representation

!!z=r(costheta+isintheta)!! is the polar representation of a complex number where !!theta!! is the angle from x-axis in anti-clockwise direction and r is the modulus of z.

Euler Form

!!z=r e^(itheta)!!is the Euler form of a complex number.

Cube roots of unity

The cube roots of unity are given by !!1, w,w^2!! which are roots of the equation !!x^3-1=0!!. This is also an important concept since we can find a question on this almost every year specially in JEE-Mains.The concept can also be extended to Nth root of unity.

Apart form this, properties of argument, modulus with their geometrical interpretation should be studied properly. All the best.

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