Complex Number Class 11

Here you will learn what is the complex number class 11 and equality of complex numbers with examples.

Let’s begin – 

Complex Number Class 11

If a, b are two real numbers, then a number of the form a + ib is called aa complex number.

Example : 7 + 2i, -1 + i, 3 – 2i, 0 + 2i, 1 + 0i etc. are complex numbers

Real and imaginary parts of a complex number : If z = a + ib is a complex number, then ‘a’ is called the real part of z and ‘b’ is known as the imaginary part of z.

The real part of z is denoted Re (z) and the imaginary part by Im (z).

Example : If z = 3 – 4i, then Re (z) = 3 and Im (z) = -4.

Purely real and purely imaginary complex numbers : A complex number z is purely real if its imaginary part is zero i.e. Im (z) = 0 and purely imaginary if its real part is zero i.e. Re (z) = 0.

Set of Complex Numbers : The set of all complex numbers is denoted by C i.e. C = {a + ib : a, b \(\in\) R}.

Since a real number ‘a’ can be written as a + 0i. Therefore, every real number is a complex number number. Hence, R \(\subset\) C, where R is the set of all real numbers.

Equality of Complex Numbers

Two Complex numbers \(z_1\) = \(a_1 + ib_1\) and \(z_2\) = \(a_2 + ib_2\)  are equal if

\(a_1\) = \(a_2\) and \(b_1\) = \(b_2\)

i.e. \(Re(z_1)\) = \(Re(z_2)\) and \(Im(z_1)\) = \(Im(z_2)\)

Example : If \(z_1\) = 2 – iy and \(z_2\) = x + 3i are equal, find x and y.

Solution : We have, 

\(z_1\) = \(z_2\)

\(\implies\) 2 – iy = x + 3i \(\implies\) 2 = x and -y = 3 \(\implies\) x = 2 and y = -3

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