Complex Number: ISC Class 11 Maths Understanding solutions Chapter-5. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe1.1, Exe-1.2, Exe-1.3, Exe-1.4, Exe-1.5, Exe-1.6, Exe-1.7, and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics..
Complex Number: ISC Class 11 Maths Understanding solutions
| Board | ISC |
| Class | 11 |
| Subject | Mathematics |
| Chapter-5 | Complex Numbers |
| Session | 2024-25 |
| Topics | Solutions of ML Aggarwal |
Complex Numbers
A complex number is a number that can be expressed in the form p + iq, where p and q are real numbers, and i is a solution of the equation
General form of Complex Number: z = p + iq
- p is known as the real part, denoted by Re z
- q is known as the imaginary part, denoted by Im z
Algebra of Complex Numbers
Addition of complex numbers : Let z1 = m + ni and z2 = o + ip be two complex numbers. Then, z1 + z2 = z = (m + o) + (n + p)i, where z = resultant complex number. For example, (12 + 13i) + (-16 +15i) = (12 – 16) + (13 + 15)i = -4 + 28i.
- The sum of complex numbers is always a complex number (closure law)
- For complex numbers z1 and z2: z2 + z1= z1 + z2 (commutative law) For complex numbers z1, z2, z3: (z1 + z2) + z3 = z1 + (z2 + z3) [associative law].
- For every complex number z, z + 0 = z [additive identity]
- To every complex number z = p + qi, we have the complex number -z = -p + i(-q), called the negative or additive inverse of z. [z + (–z) = 0]
Difference of complex numbers : Let z1 = m + ni and z2 = o + ip be two complex numbers, then z1 – z2 = z1 + (-z2). For example, (16 + 13i) – (12 – 1i) = (16 + 13i) + (-12 + 1i ) = 4 + 14i and (12 – 1i) – (16 + 13i) = (12 – 1i) + ( -16 – 13i) = -4 – 14i
Multiplication of complex numbers : Let z1 = m + ni and z2 = o + ip be two complex numbers then, z1 × z2 = (mo – np) + i(no + pm). For example, (2 + 4i) (1 + 5i) = (2 × 1 – 4 × 5) + i(2 × 5 + 4 × 1) = -22 + 14i The product of two complex numbers is a complex number (closure law)
The Modulus and Conjugate of Complex Numbers
Let z = m + in be a complex number. Then, the modulus of z, denoted by |z| =
is the distance between the point (m, n) and the origin (0, 0). The x-axis is termed as the real axis and the y-axis is termed as the imaginary axis.
To know more about Modulus and Conjugate of Complex Numbers
Exe-5.1
Complex Numbers ML Aggarwal ISC Class-11 Maths Ch-5
Exe-5.2
Complex Numbers ML Aggarwal ISC Class-11 Maths Ch-5
Exe-5.3
Complex Numbers ML Aggarwal ISC Class-11 Maths Ch-5
Exe-5.4
Complex Numbers ISC Class-11 Maths Ch-5
Exe-5.5
Exe-5.6
ML Aggarwal ISC Class-11 Maths Ch-5
Exe-5.7
Complex Numbers ISC Class-11 Maths Ch-5
Chapter Test
Ch-5 Complex Numbers of ML Aggarwal ISC Class-11 Maths
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