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Find the value of z if z^2 = -16.
Find the value of z if z^2 = -16.
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Practice Questions
1 question
Q1
Find the value of z if z^2 = -16.
4i
-4i
4
-4
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Taking square root, z = ±√(-16) = ±4i.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the value of z if z^2 = -16.
Solution:
Taking square root, z = ±√(-16) = ±4i.
Steps: 7
Show Steps
Step 1: Start with the equation z^2 = -16.
Step 2: To find z, we need to take the square root of both sides.
Step 3: When taking the square root of -16, we can rewrite it as √(-16).
Step 4: Since the square root of a negative number involves 'i' (the imaginary unit), we can express it as √(16) * √(-1).
Step 5: We know that √(16) = 4 and √(-1) = i.
Step 6: Therefore, √(-16) = 4i.
Step 7: Since we have both positive and negative roots, we write z = ±4i.
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