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 = ā-1. Using this logic, 7 + 12i is a complex quantity in which 7 is the real part and 12i ā is the imaginary part.
How to Get the Negative Sign Out of Square Root
Suppose a complex number:
C = ā-a2
then,
ā-a2 = ā(-1ĆaĆa) = ā(-1)Ćā(aĆa) = i Ć a = ai
Question: Simplify the number using the imaginary unit i: Square root of -16.
Answer:
Given: C = ā-16
This can be simplified as:
ā-16 = ā(-1Ć4Ć4)
= ā(-1)Ćā(4Ć4)
= i Ć 4
= 4i
Similar Questions
Question 1: Simplify the number using the imaginary unit i: Square root of -49.
Answer:
Given: C = ā-49
This can be simplified as:
ā-49 = ā(-1Ć7Ć7)
= ā(-1)Ćā(7Ć7)
= i Ć 7
= 7i
Question 2: Simplify the number using the imaginary unit i: square root of -512.
Answer:
Given: C = ā-49
This can be simplified as:
ā-512 = ā(-1Ć8Ć8Ć8)
= ā(-1)Ćā(8Ć8)Ćā8
= i Ć 8 Ć ā(2Ć2Ć2)
= i Ć 8 Ć 2 Ć ā2
= 16ā2i
Question 3: Simplify the number using the imaginary unit i: square root of -100.
Answer:
Given: C = ā-100
This can be simplified as:
ā-100 = ā(-1Ć10Ć10)
= ā(-1)Ćā(10Ć10)
= i Ć 10
= 10i
Question 4: Simplify the number using the imaginary unit i: square root of -81.
Answer:
Given: C = ā-81
This can be simplified as:
ā-49 = ā(-1Ć9Ć9)
= ā(-1)Ćā(9Ć9)
= i Ć 9
= 9i
Question 5: Simplify the number using the imaginary unit i: square root of -729.
Answer:
Given: C = ā-729
This can be simplified as:
ā-729 = ā(-1Ć27Ć27)
= ā(-1)Ćā(27Ć27)
= i Ć 27
= 27i