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 = β-1. Using this logic, 7 + 12i is a complex quantity in which 7 is the real part and 12i β is the imaginary part.
How to Get the Negative Sign Out of Square Root
Suppose a complex number:
C = β-a2
then,
β-a2 = β(-1ΓaΓa) = β(-1)Γβ(aΓa) = i Γ a = ai
Question: Simplify the number using the imaginary unit i: Square root of -16.
Answer:
Given: C = β-16
This can be simplified as:
β-16 = β(-1Γ4Γ4)
= β(-1)Γβ(4Γ4)
= i Γ 4
= 4i
Similar Questions
Question 1: Simplify the number using the imaginary unit i: Square root of -49.
Answer:
Given: C = β-49
This can be simplified as:
β-49 = β(-1Γ7Γ7)
= β(-1)Γβ(7Γ7)
= i Γ 7
= 7i
Question 2: Simplify the number using the imaginary unit i: square root of -512.
Answer:
Given: C = β-49
This can be simplified as:
β-512 = β(-1Γ8Γ8Γ8)
= β(-1)Γβ(8Γ8)Γβ8
= i Γ 8 Γ β(2Γ2Γ2)
= i Γ 8 Γ 2 Γ β2
= 16β2i
Question 3: Simplify the number using the imaginary unit i: square root of -100.
Answer:
Given: C = β-100
This can be simplified as:
β-100 = β(-1Γ10Γ10)
= β(-1)Γβ(10Γ10)
= i Γ 10
= 10i
Question 4: Simplify the number using the imaginary unit i: square root of -81.
Answer:
Given: C = β-81
This can be simplified as:
β-49 = β(-1Γ9Γ9)
= β(-1)Γβ(9Γ9)
= i Γ 9
= 9i
Question 5: Simplify the number using the imaginary unit i: square root of -729.
Answer:
Given: C = β-729
This can be simplified as:
β-729 = β(-1Γ27Γ27)
= β(-1)Γβ(27Γ27)
= i Γ 27
= 27i
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