Question

If f(z)=dfrac7-z1-z², where z=1+2i, then |f(z)| is equal to

• A. (|z|)/(2)
• B. |z|
• C. 2|z|
• D. None of these

Hint:

Use |z₁/z₂|=(|z₁|)/(|z₂|) for complex modulus problems.

Answer 1

The Correct Option is A

|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)