Question 1: Find the square root of the following complex numbers:

Answer:

There are two ways by which we can solve the problems. We have a few solved by each method.

Squaring both sides

… … … … … i)

… … … … … ii)

… … … … … iii) [ since ]

Solving i) and iii)

Since is positive, therefore and are of same signs.

Here , therefore

Here , therefore

Here , therefore

Here , therefore

Squaring both sides

… … … … … i)

… … … … … ii)

… … … … … iii) [ since ]

Solving i) and iii)

Since is negative, therefore and are of opposite signs.

Squaring both sides

… … … … … i)

… … … … … ii)

… … … … … iii) [ since ]

Solving i) and iii)

Since is positive, therefore and are of same signs.

Here , therefore

Here , therefore