Square Root of a Complex Number A complex number is a number of the form a + bi, where a and b are real numbers. The square root of a complex number, denoted...
A complex number is a number of the form a + bi, where a and b are real numbers. The square root of a complex number, denoted by ā(a + bi), is a complex number that is the square root of the original complex number.
The square root operation can be applied to both real and imaginary parts of a complex number. For example, ā(a + bi) = āa + āb.
The square root of a complex number can be found by using the following formula:
ā(a + bi) = āa - āb
Example:
ā(2 + 3i) = ā2 - ā3i
The triangle inequality states that in any triangle, the length of the longest side (c) is less than or equal to the sum of the lengths of the other two sides (a and b).
In other words, c ā¤ a + b.
The triangle inequality can be applied to complex numbers in the following way:
ā(a + bi) ā¤ āa + āb
Example:
ā(a + bi) ā¤ āa - āb
Note:
The triangle inequality is not applicable to negative numbers