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NCERT Class XI Mathematics - Complex Numbers and Quadratic Equations - Solutions

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Question : 12 of 52
Marks: +1, -0
5+3i\sqrt{5}+3i
Solution:  
Let z = 5+3i\sqrt{5}+3i
Then z−\overset{-}{z} = 5−3i\sqrt{5}-3i ... (i)
and ∣z∣2|z|^2 = (5)2+(3)2(\sqrt{5})^2+(3)^2 = 14 ... (ii)
∴ The multiplicative inverse of 5+3i\sqrt{5}+3i is given by :
z−1z^{-1} = z−∣z∣2\frac{\overset{-}{z}}{|z|^2} = 5−3i14\frac{\sqrt{5}-3i}{14} (By using (i) and (ii))
= 514+i−314\frac{\sqrt{5}}{14}+i\frac{-3}{14}
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