AP EAMCET · Maths · Complex Number
If \(a, b \in R\) and \(i=\sqrt{-1}\), then the number of ordered pairs of real numbers \((a, b)\) satisfying the condition \((a+b i)^3=a-b i\) is
- A 3
- B 2
- C 4
- D 5
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
Given condition, \[ \begin{aligned} & (a+b i)^3=a-b i \\ & \text { i.e. } a^3+i^3 b^3+3 a^2 b i-3 a b^2 i^2=a-b i \\ & \Rightarrow \quad a^3-i b^3+i 3 a^2 b-3 a b^2=a-b i \\ & \left(a^3-3 a b^2\right)-i\left(b^3-3 a^2 b\right)=a-b i \\ & \end{aligned} \] Equating the…
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