alleryStart learning →Using de Moivre's formula, what is (cos 30 + i sin 30) raised to the power 6, angles in degrees?
- -1
- 1
- i
- -i
Show answer and solution
Correct answer: A. -1
The argument becomes 6 times 30 = 180 degrees, giving cos 180 + i sin 180 = -1.
MHT-CET Complex Numbers and Quadratic Equations — practice questions — page 3
Explore 72 free Complex Numbers and Quadratic Equations questions in MHT-CET Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Complex Numbers and Quadratic Equations with Quill →Complex Numbers and Quadratic Equations questions and exercises with answers
Showing questions 61–72 of 72.
Using de Moivre's formula, what is (cos 30 + i sin 30) raised to the power 6, angles in degrees?Read the answer and worked solution →How many distinct complex fourth roots does the number 1 have?Read the answer and worked solution →A nonzero complex number has how many distinct n-th roots?Read the answer and worked solution →Which number set contains a root of every non-constant polynomial equation?Read the answer and worked solution →The equation x^2 + 4 = 0 has no real root. What are its complex roots?Read the answer and worked solution →The roots of x^2 + 2x + 5 = 0 are which pair?Read the answer and worked solution →The polynomial x^2 - 2 has no root in which set?Read the answer and worked solution →The complex numbers form a real vector space of what dimension?Read the answer and worked solution →Geometrically, multiplying by a complex number does what to the plane?Read the answer and worked solution →Adding two complex numbers on the plane gives the fourth vertex of which shape?Read the answer and worked solution →Evaluate (2 + 3i)(1 - i) and write the result in the form a + bi.Read the answer and worked solution →What is the real part of (2 + i) squared?Read the answer and worked solution →
Worked practice questions
How many distinct complex fourth roots does the number 1 have?
- 1
- 2
- 4
- 8
Show answer and solution
Correct answer: C. 4
A nonzero number has exactly n distinct n-th roots, so 1 has four fourth roots: 1, i, -1 and -i.
A nonzero complex number has how many distinct n-th roots?
- n
- n + 1
- 2n
- 1
Show answer and solution
Correct answer: A. n
The periodicity of sine and cosine gives exactly n different values for the n-th root of a nonzero number.
How to practise
- Choose a Complex Numbers and Quadratic Equations question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.