Complex Numbers
A complex number is a number that can be expressed in the form z = a + bi
Now a and b are real numbers while i is the imaginary unit satisfies the equation I*I = -1

In this expression a is the real part and b is the imaginary part of the complex number.
In a complex number if the real part is zero then it is said to be purely imaginary. Also if the imaginary part is zero the it is a real number

Q1. Find the value of x this equation�
X²+1 = 0
Ans. X = +i or -i

Q2. Solve the quadratic equation:
x² + 4 = 0

Ans. Since x² +4=0 then x² =−4 and x =√(−4)
i.e., x = (−1)(4) = √−1√4 = i (±2)
= ± 2i, (since i = √−1)

The equation x2 = 1 has two roots x = 1 and x = −1.
The equation x2 = −1 has no roots because you cannot take the square root
of a negative number.
X = √(-1)
Then we say i = √(-1) and i² = -1

Q3. Solve the quadratic equation:
2x² + 3x + 5 = 0

It quite hard to post equations here i will attach screenshots

Q4. Problem 3. Evaluate
(a) j 3 (b) j 4 (c) j 23 (d) −4/j 9