The sum of the real parts of the complex numbers satisfying the equations z − 2 i z − 4 i = 1 and z + 3 i z − 8 + 3 i = 5 3 is 5 k , find k .

Question

The sum of the real parts of the complex numbers satisfying the equations ​ z − 2 i z − 4 i ​ ​ = 1 and ​ z + 3 i z − 8 + 3 i ​ ​ = 5 3 ​ is 5 k ​ , find k .

TestHub · Accepted Answer

​ z − 2 i z − 4 i ​ ​ = 1 ⇒ z = x + 3 i using this in ​ z + 3 i z − 8 + 3 i ​ ​ = 5 3 ​ ⇒ 5∣ x − 8 + 6 i ∣ = 3∣ x + 6 i ∣ ⇒ x = 8 , 17 Two complex numbers 8+3i, 17+3i Sum of real part = 8 + 17 = 25

Mathematics - Complex Number Question with Solution | TestHub

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