Simplify the Square root of -16 using the imaginary unit i
A complex number is written as a + ib, where a is the real part and ib is the imaginary unit such that i = √-1. Using this logic, 7 + 12i is a complex quantity in which 7 is the real part and 12i – is the imaginary part.
Â
How to Get the Negative Sign Out of Square Root
Suppose a complex number:Â
C = √-a2
then,
√-a2 = √(-1×a×a) = √(-1)×√(a×a) = i × a = ai
Question: Simplify the number using the imaginary unit i: Square root of -16.
Answer:
Given: C = √-16
This can be simplified as:
√-16 = √(-1×4×4)Â
= √(-1)×√(4×4)Â
= i × 4Â
= 4i
Similar Questions
Question 1: Simplify the number using the imaginary unit i: Square root of -49.
Answer:
Given: C = √-49
This can be simplified as:
√-49 = √(-1×7×7)Â
= √(-1)×√(7×7)Â
= i × 7Â
= 7i
Question 2: Simplify the number using the imaginary unit i: square root of -512.
Answer:
Given: C = √-49
This can be simplified as:
√-512 = √(-1×8×8×8)Â
= √(-1)×√(8×8)×√8Â
= i × 8 × √(2×2×2)
= i × 8 × 2 × √2
= 16√2i
Question 3: Simplify the number using the imaginary unit i: square root of -100.
Answer:
Given: C = √-100
This can be simplified as:
√-100 = √(-1×10×10)Â
= √(-1)×√(10×10)Â
= i × 10
= 10i
Question 4: Simplify the number using the imaginary unit i: square root of -81.
Answer:
Given: C = √-81
This can be simplified as:
√-49 = √(-1×9×9)Â
= √(-1)×√(9×9)Â
= i × 9Â
= 9i
Question 5: Simplify the number using the imaginary unit i: square root of -729.
Answer:
Given: C = √-729
This can be simplified as:
√-729 = √(-1×27×27)Â
= √(-1)×√(27×27)Â
= i × 27Â
= 27i
Last Updated :
25 Dec, 2023
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