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KCET Complex Numbers — practice questions — page 2

Explore 56 free Complex Numbers questions in KCET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Complex Numbers questions and exercises with answers

Showing questions 31–56 of 56.

Find principal argument of -1 - i:Read the answer and worked solution →For roots of unity ω^n = 1: which is the SMALLEST n such that 1 + ω + ω² + ... + ω^(n-1) = 0?Read the answer and worked solution →Solve: z² + z + 1 = 0:Read the answer and worked solution →If z1, z2, z3 are vertices of an equilateral triangle, then:Read the answer and worked solution →Find (3 + 4i)/(1 + 2i):Read the answer and worked solution →SAT · Mathematics · Complex Numbers — T/FRead the answer and worked solution →Quadratic discriminant — true or false?Read the answer and worked solution →Sort: does the quadratic have real or complex roots?Read the answer and worked solution →Match the complex number form to its representationRead the answer and worked solution →Which complex number has the larger modulus?Read the answer and worked solution →Spot the value that is NOT purely imaginaryRead the answer and worked solution →Type the value of each expressionRead the answer and worked solution →Real part or imaginaryRead the answer and worked solution →Modulus or conjugateRead the answer and worked solution →Type the complex termRead the answer and worked solution →Which operation obeys itRead the answer and worked solution →Pop what sits on the real axisRead the answer and worked solution →One word is wrongRead the answer and worked solution →Order the reason for extendingRead the answer and worked solution →Which one does not belongRead the answer and worked solution →Real or complex onlyRead the answer and worked solution →Spot the false statementRead the answer and worked solution →Which ones belongRead the answer and worked solution →Knock out the true statementsRead the answer and worked solution →Match each complex number partRead the answer and worked solution →Key in the power of iRead the answer and worked solution →

Worked practice questions

Find principal argument of -1 - i:

  1. -π/4
  2. -3π/4
  3. 3π/4
  4. π/4
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Correct answer: B. -3π/4

-1 - i is at (-1, -1), in third quadrant. Principal argument range (-π, π]: arg = -3π/4 (or equivalently +5π/4, but principal value is in (-π, π]).

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For roots of unity ω^n = 1: which is the SMALLEST n such that 1 + ω + ω² + ... + ω^(n-1) = 0?

  1. 2
  2. Only n = 3
  3. 1
  4. Any n > 1
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Correct answer: D. Any n > 1

Sum 1 + ω + ω² + ... + ω^(n-1) = (ω^n - 1)/(ω - 1) = 0 when ω is a primitive n-th root (ω ≠ 1). **So for any n ≥ 2 (with non-trivial primitive root), sum is 0.**

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Solve: z² + z + 1 = 0:

  1. z = ±i
  2. z = ±1
  3. z = (-1 ± i√3)/2 (complex cube roots of unity other than 1)
  4. No solution
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Correct answer: C. z = (-1 ± i√3)/2 (complex cube roots of unity other than 1)

z = (-1 ± √(1 - 4))/2 = (-1 ± √(-3))/2 = (-1 ± i√3)/2. These are ω and ω² (complex cube roots of unity).

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