Euler’s formula (HSC SSCE Mathematics Extension 2): Quizzes
📚Quizzes
Practise the questions
10 questions from this quiz
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Practise the questions
10 questions from this quiz
According to Euler's formula, e^{iθ} equals?
According to Euler's formula, e^{iθ} equals?
cosθ + i sinθ
What is the exact value of e^{iπ}?
What is the exact value of e^{iπ}?
-1
Which substitution into e^x's series gives Euler's formula?
Which substitution into e^x's series gives Euler's formula?
Replace x by ix
What is e^{iα}·e^{iβ} equal to?
What is e^{iα}·e^{iβ} equal to?
e^{i(α+β)}
Geometric effect of multiplying by e^{iθ}?
Geometric effect of multiplying by e^{iθ}?
Rotate by θ radians
Which is the statement of De Moivre's theorem?
Which is the statement of De Moivre's theorem?
(cosθ + i sinθ)^n = cos nθ + i sin nθ
Which formula gives sinθ in exponentials?
Which formula gives sinθ in exponentials?
(e^{iθ}-e^{-iθ})/(2i)
If z = r e^{iθ}, what is z^n?
If z = r e^{iθ}, what is z^n?
r^n e^{inθ}
Using Euler's formula, what is e^{iπ} equal to?
Using Euler's formula, what is e^{iπ} equal to?
-1
Geometrically, multiplying a complex number by e^{iθ} does what?
Geometrically, multiplying a complex number by e^{iθ} does what?
Rotates the point by θ radians