COMEDK · Maths · 3. Complex Number
If \((\sqrt{3}+i)^{100}=2^{99}(a+i b)\), then \(a^{2}+b^{2}\) is equal to
- A \(\sqrt{2}\)
- B 4
- C \(\sqrt{3}\)
- D None of these
Answer & Solution
Correct Answer
(B) 4
Step-by-step Solution
Detailed explanation
Given the expression \((\sqrt{3} + i)^{100} = 2^{99}(a + ib)\). Express the complex number \(z = \sqrt{3} + i\) in polar form. The modulus is \(r = |\sqrt{3} + i| = \sqrt{(\sqrt{3})^2 + 1^2} = \sqrt{3 + 1} = 2\). The argument \(\theta\) is given by…
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