12th Maths Guide Chapter 2 Complex Numbers Exercise 2.5 PDF Solution

Question no 1:

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Question no 2: For any two complex numbers z₁ and z₂, such that |z₁| = |z₂| = 1 and z₁ z₂ ≠ -1, then show that

Question no 3: Which one of the points 10 – 8i, 11 + 6i is closest to 1 + i.

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Question no 4: If |z| = 3, show that 7 ≤ |z + 6 – 8i| ≤ 13.

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Question no 5: If |z| = 1, show that 2 ≤ |z² – 3| ≤ 4.

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Question no 6: If |z| = 2 show that the 8 ≤ |z + 6 + 8i| ≤ 12

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Question no 7: If z₁ z₂ and z₃ are three complex numbers such that |z₁| = 1, |z₁| = 2, |z₃| = 3 and |z₁ + z₂ + z₃| = 1 show that |9z₁ z₂ + 4z₁ z₃ + z₂ z₃| = 6.

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Question no 8: If the area of the triangle formed by the vertices z, iz, and z + iz is 50 square units, find the value of |z|.

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Question no 9: Show that the equation z³ + 2 z¯ = 0 has five solutions.

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Question no 10: Find the square roots of following.

(i) 4 + 3i

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(ii) -6 + 8i

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(iii) -5 – 12i

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