Question

If $Z = \frac {(\sqrt {3}+ i)^3 (3i+4)^2}{{(8+6i)^2}}$ then $|Z|$ is equal to

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

2

Answer 2

Z = $\frac{(√3 + 1)^2(3i+4)^2 }{(8+6i)^2}$ ,

Then using identity |a+ib| = √a2 +b2

and $\frac{|Z_1Z_2|}{|Z_3|}=\frac{|Z_!||Z_2|}{|Z_3|}$

Therefore,

|Z| = $|\frac{(√3 + 1)^2(3i+4)^2 }{(8+6i)^2}|$

= $\frac{|(√3 + 1)^2||(3i+4)^2| }{(8+6i)^2}$

= $\frac{2^3.5^3}{10^2}$

= 2