Simplify (3 + i)/2 + (1 – i)/4

Last Updated : 22 Dec, 2023

Complex numbers are those with the formula a + ib, where a and b are real numbers and I (iota) is the imaginary component and represents (-1), and are often represented in rectangle or standard form. 10 + 5i, for example, is a complex number in which 10 represents the real component and 5i represents the imaginary part. Depending on the values of a and b, they might be wholly real or purely fictitious. When a = 0 in a + ib, ib is a totally imaginary number, and when b = 0, we get a, which is a strictly real number.

Addition of Complex Numbers

Adding two complex numbers is similar to that of the addition of two real numbers, the only difference being that one has to separate the real and imaginary parts in order to add two complex numbers. Say, if z₁ = a + ib and z₂ = c + id, then

z₁ + z₂ = a + ib + c + id

= (a + c) + i(b + d)

Simplify (3 + i)/2 + (1 – i)/4

Solution:

$\frac{(3+i)}2+\frac{(1 - i)}4=\frac{3}2+\frac{i}2+\frac{1}4-\frac{i}{4}$

= $\frac{3}2+\frac{1}4+\frac{i}2-\frac{i}{4}$

= $\frac{6}4+\frac{1}4+i[\frac{2}4-\frac{1}{4}]$

= $\frac{7}4+i[\frac{1}4]$