How many complex numbers satisfy ?
Answer and explanation
Correct answer: B. 9
**Why not the others: The count 8 accounts only for roots on the unit circle while forgetting the trivial solution , and other values arise from incorrect algebraic degree reductions.
- Step 1: Take the modulus on both sides of : .
- Step 2: Rearrange to solve for : , giving or . The root yields the single solution .
- Step 3: For , recall that . Substituting gives . Because , the equation possesses exactly distinct roots on the unit circle.
- Step 4: Combining the roots on the unit circle with the origin solution gives solutions.
Answer
9.
Practise more Complex numbers.
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