Question:
If f(z)=dfrac7-z1-z², where z=1+2i, then |f(z)| is equal to
If f(z)=dfrac7-z1-z², where z=1+2i, then |f(z)| is equal to
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Use |z₁/z₂|=(|z₁|)/(|z₂|) for complex modulus problems.
Updated On: Mar 19, 2026
- (|z|)/(2)
- |z|
- 2|z|
- None of these
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The Correct Option is A
Solution and Explanation
|f(z)|=(|7-z|)/(|1-z²|)
For z=1+2i:
|z|=√(1²+2²)=√(5)
|7-z|=|6-2i|=√(36+4)=√(40)
z²=(1+2i)²=-3+4i ⟹ |1-z²|=|4-4i|=√(32)
|f(z)|=frac√(40)√(32)=√((5)/(4))=frac√(5)2
=(|z|)/(2)
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