Exponential Form (AQA A-Level Further Maths): Quizzes

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Exponential Form
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10 questions from this quiz

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What is Euler's formula?

eiθ=cosθ+isinθe^{i\theta} = \cos\theta + i\sin\theta

What is the required range for the argument θ\theta in exponential form reiθre^{i\theta}?

π<θπ-\pi < \theta \leq \pi

What is 3eπi3e^{\pi i} in Cartesian form a+bia + bi?

3-3

What is the modulus of the complex number z=4+3iz = 4 + 3i?

55

Express cosθ\cos\theta using exponential form.

eiθ+eiθ2\frac{e^{i\theta} + e^{-i\theta}}{2}

Express sinθ\sin\theta using exponential form.

eiθeiθ2i\frac{e^{i\theta} - e^{-i\theta}}{2i}

If z1=2eiπ/3z_1 = 2e^{i\pi/3} and z2=3eiπ/6z_2 = 3e^{i\pi/6}, what is z1z2z_1z_2?

6eiπ/26e^{i\pi/2}

If z1=8eiπ/4z_1 = 8e^{i\pi/4} and z2=2eiπ/6z_2 = 2e^{i\pi/6}, what is z1z2\frac{z_1}{z_2}?

4eiπ/124e^{i\pi/12}

What is eiθe^{-i\theta} equal to?

cosθisinθ\cos\theta - i\sin\theta

For z=2+3iz = -2 + 3i, which quadrant determines the sign of the argument?

Second quadrant

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