Writing Complex Numbers in Polar Form (Leaving Cert Mathematics): Quizzes

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Writing Complex Numbers in Polar Form
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In polar form z=r(cos⁡θ+isin⁡θ)z = r(\cos{\theta} + i\sin{\theta}), what does rr represent?

The modulus of zz

What is the formula for the modulus of a complex number z=a+biz = a + bi?

r=a2+b2r = \sqrt{a^2 + b^2}

Polar form is especially useful for which operations on complex numbers?

Multiplication, division, exponentiation

What is the modulus of z=2+3iz = 2 + 3i?

13\sqrt{13}

What is the modulus of z=−3+3iz = -3 + \sqrt{3}i?

232\sqrt{3}

For a complex number in quadrant 2, what is θ\theta in radians if the base angle is AA?

θ=π−A\theta = \pi - A

For a complex number in quadrant 3, what is θ\theta in radians if the base angle is AA?

θ=π+A\theta = \pi + A

For a complex number in quadrant 4, what is θ\theta in degrees if the base angle is AA?

θ=360°−A\theta = 360° - A

For z=−3+3iz = -3 + \sqrt{3}i with base angle π6\frac{\pi}{6} in quadrant 2, what is θ\theta?

5π6\frac{5\pi}{6}

What geometric shape does a complex number outline on the Argand diagram?

A right-angled triangle

A complex number z=a+biz = a + bi with a<0a < 0 and b>0b > 0 lies in which quadrant?

Quadrant 2

Explore Leaving Cert Mathematics Revision Notes by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Model Answers by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Flashcards by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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