Let z be a complex number such that the real part of z + 2 i z − 2 i is zero. Then, the maximum value of ∣ z − ( 6 + 8 i ) ∣ is equal to

Question

Let z be a complex number such that the real part of z + 2 i z − 2 i ​ is zero. Then, the maximum value of ∣ z − ( 6 + 8 i ) ∣ is equal to

TestHub · Accepted Answer

​ z + 2 i z − 2 i ​ + z − 2 i z + 2 i ​ = 0 z z − 2 i z − 2 iz + 4 ( − 1 ) + z z + 2 z i + 2 z i + 4 ( − 1 ) = 0 ⇒ 2∣ z ∣ 2 = 8 ⇒ ∣ z ∣ = 2 ∣ z − ( 6 + 8 i ) ∣ maximum ​ = 10 + 2 = 12 ​

Mathematics - Complex Number Question with Solution | TestHub

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