Question

Properties of Subtraction :
1) Z - z = 2 Im(z) (Verify)
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Answer 1

Step-by-step explanation:

The Complex Algebra

In basic algebra of numbers, we have four operations namely – addition, subtraction, multiplication and division. As we will see in a bit, we can combine complex numbers with them. Let z1 and z2 be any two complex numbers and let, z1 = a+ib and z2 = c+id.

Imaginary Numbers

Example: Schrodinger Equation which governs atoms is written using complex numbers

Addition and Subtraction of Imaginary Numbers

The addition of two complex numbers is defined as:

z1 + z2 = (a + ib) ± (c + id) = (a + c) ± i(b + d)

Which gives another complex number whose real part is Re(z1) + Re(z2) = a + c and imaginary part of the new complex number = Im(z1) + Im(z2) = b + d. For example, on adding 2 and 3 + 4i, we can write 2 as 2 + 0*i and therefore, 2 + (3+4i) = (2+3) + i(0+4) = 5 + i.4

Browse more Topics under Complex Numbers And Quadratic Equations

Basics of Complex Numbers

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