RS Aggarwal Class 11 Solutions Chapter-5 Complex Numbers and Quadratic Equations

• The Complex Number Class 11 RS Aggarwal solutions talk about what complex numbers are. A complex number is nothing but a number that can be expressed in the form of p+iq. This is where both p and q are real numbers, and i is the solution of any equation. The numbers 8+2i and 2+3i are examples of complex numbers.

• Generally, the complex number will be represented as z = p + iq

• Here p is the real part that is denoted by Re z and q is the imaginary part, and it is denoted by Im z

• A complex number will be purely real when its imaginary part is equal to 0.

• The complex number also follows the concept of equality,

• Two complex numbers z1 = a1 + ib1 and z2 = a2 + ib2 are equal, if a1= a2 and b1 = b2 i.e., Re (z1) = Re (z2) and Im (z1) = Im (z2).

• The complex number can also be added. Suppose there are two numbers like Let z1 = m + ni and z2 = o + ip. These are two kinds of complex numbers. You can add both zi and z2. So basically z1 + z2 = z = (m + o) + (n + p)I and z that is obtained is the complex number that is obtained.

• The sum of complex numbers will always be a complex number as per the closure law.

• For complex numbers z1 and z2: z2 + z1= z1 + z2 as per the commutative law)

•  For complex numbers z1, z2, z3: (z1 + z2) + z3 = z1 + (z2 + z3) . This is the associative law.

• For every complex number z, z + 0 = z. This is the additive identity

• To every complex number z = p + qi, then we have the complex number -z = -p + i(-q), called the negative or additive inverse of z.

• z+(–z)=0

• z+(–z)=0

• The complex numbers can also be subtracted from each other. So if there are two complex numbers z1 = m + ni and z2 = o + ip then you can calculate z1 – z2 = z1 + (-z2).

• Complex numbers can also be multiplied. If z1 = m + ni and z2 = o + ip are two complex numbers then z1 × z2 = (mo – np) + i(no + pm)

• For the complex number multiplication, you need to remember these.

• For complex numbers z1 and z2, z1 × z2 = z2 × z1 (commutative law).

• For complex numbers z1, z2, z3, (z1 × z2) × z3 = z1 × (z2 × z3)

• associative law

• associative law.

• Here are the properties of complex number multiplication

• Commutative z1z2 = z2z1

• (ii) Associative (z1 z2) z3 = z1(z2 z3)

• (iii) Multiplicative Identity z • 1 = z = 1 • z

• Here, 1 is the multiplicative identity of an element z.

• (iv) Multiplicative Inverse Every non-zero complex number z there exists a complex number z1 such that z.z1    = 1 = z1 • z

• (v)  Distributive Law

• (a)  z1(z2 + z3) = z1z2 + z1z3  (left distribution)

• (b) (z2 + z3)z1 = z2z1 + z3z1 (right distribution)

Also when z1 = m + in and z2 = o + ip. Then,

• z1 + z2 = (m + o) + i (n + p)

• z1 z2 = (mo – np) + i(mp + on)

• The conjugate of any complex number z = m + in, denoted by z¯¯¯, is given by z = m – in.

The modulus and the conjugate of complex numbers state that when z = m + in is a complex number then the modulus of z, denoted by |z| = m2−n2−−−−−−−√ and the conjugate of z, denoted by z¯¯¯ is the complex number m – ni.

Preparation Tips for RS Aggarwal Class 11 Math Chapter 5

• Practicing these solutions on Complex Numbers is important because it forms the key part in building basics to perform well in mathematics in higher classes.

• Going through these RS Aggarwal Class 11 Solutions Complex Numbers solutions will get you prepared to do complex problems on complex numbers with ease either in your school or competitive examinations

• The topic is covered with detailed solutions on this website that builds on your confidence.

RS Aggarwal Class 11 Solutions Chapter-5 Complex Numbers and Quadratic Equations are a must for those students who are having trouble with the chapter concepts. Quadratic Equation is not only an important concept from the CBSE exams point of view but is also an important part of a lot of exams such as NEET, JEE, IPU-CET, etc. Chapter 5 of RS Aggarwal Solutions will provide you with a detailed idea regarding the topics involved such as the arithmetic operations on complex numbers, finding roots of quadratic equations, and determining their nature. RS Aggarwal Class 11 Solutions Chapter-5 Complex Numbers and Quadratic Equations provides a deep analysis of the chapter along with various handy examples.  

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If you want to solve the questions from the exercises of Chapter 5 Complex Numbers and Quadratic Equations then it is highly recommended to check out RS Aggarwal Class 11 Solutions Chapter-5 Complex Numbers and Quadratic Equations for all the solutions that you wish for.

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