
Find the square root of complex number 9 + 40i
Answer
527.4k+ views
3 likes
Hint: To find the square root of a complex number, we will assume the root to be a + ib. Then we can compare it with the original number to find the values of a and b, which will give us the square root.
Complete step-by-step solution -
Let 9 + 40i =
We will simplify this equation, by proceeding as-
We know that = -1
By comparing the real and imaginary parts-
............. (1)
………………...(2)
Using equation (1) we can write that
Substituting this value in (2)-
Squaring both sides of the equation,
= 0
= 16, = -25 (rejected because square cannot be negative)
b = 4, -4
Substituting the value of b in equation (1)-
- 16 = 9
= 25
a = 5, -5
So, the square roots of are and .
This is the required answer.
Note: The most common mistake is that students only write one of the roots and do not write the other one. We should always take all the possible cases and reject them as and when required.
Complete step-by-step solution -
Let 9 + 40i =
We will simplify this equation, by proceeding as-
We know that
By comparing the real and imaginary parts-
Using equation (1) we can write that
Substituting this value in (2)-
Squaring both sides of the equation,
b = 4, -4
Substituting the value of b in equation (1)-
a = 5, -5
So, the square roots of
This is the required answer.
Note: The most common mistake is that students only write one of the roots and do not write the other one. We should always take all the possible cases and reject them as and when required.
Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
School Full course for CBSE students
₹41,848 per year
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
Why should a magnesium ribbon be cleaned before burning class 12 chemistry CBSE

A renewable exhaustible natural resources is A Coal class 12 biology CBSE

Megasporangium is equivalent to a Embryo sac b Fruit class 12 biology CBSE

What is Zeises salt and ferrocene Explain with str class 12 chemistry CBSE

How to calculate power in series and parallel circ class 12 physics CBSE

Anal style is present in A Male cockroach B Female class 12 biology CBSE
