SHORTCUT TO FIND SQUARE ROOT OF COMPLEX NUMBER

In this section, we are going to see the shortcut or formula to find the square root of a complex number.

Let z = a + ib, where a and b are real numbers.

Formula to find square root of the complex number z :

Video Lesson

Problem 1 :

Find the square roots of (4 + 3i).

Solution :

Let z = 4 + 3i.

Comapring (a + bi) and (4 + 3i), we get

a = 4 and b = 3

Substitute |z| = 5, a = 4 and b = 3 into the above formula.

Problem 2 :

Find the square roots of (-6 + 8i).

Solution :

Let z = -6 + 8i.

Comapring (a + bi) and (-6 + 8i), we get

a = -6 and b = 8

Substitute |z| = 10, a = -6 and b = 8 into the above formula.

Example 3 :

Find the square roots of (-5 - 12i).

Solution :

Let z = -5 - 12i.

Comapring (a + bi) and (-5 - 12i), we get

a = -5 and b = -12

Substitute |z| = 13, a = -5 and b = -12 into the above formula.

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