Question

The least value of |z| where z is complex number which satisfies the inequality

exp \(\bigg(\frac{(|z|+3)(|z|-1)}{\big||z|+1 \big|}log_{e^2}\bigg)\) \(\geq log_\sqrt{2}\big|5\sqrt{7}+9i \big|,\)

\(i=\sqrt{-1},\) is equal to:

(1) 3

(2) \(\sqrt{5}\)

(3) 2

(4) 8

Answer 1

Correct answer is (1)

Comments

Can you please explain me the second step? Where did exp go? And how does  log|5 rt7+9i| became log(16)? Please explain. _/\_

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Exp has no meaning in these question.
Ignore it.
And
(5√7 +9i) is converted  to polar form i.e. =16(cos 9/5√7 + i sin 9/5√7)
 = 16(0.999  + i * 0.00)   
= 16

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|5√7+9i|=√((5√7)^2+9^2)=√(175+81)=√256=16 and exp is antilog function and we use here log(a^b) =b log a.