Modulus & Argument (Edexcel A-Level Further Mathematics): Quizzes

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Modulus & Argument
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What does the modulus z|z| of a complex number represent on an Argand diagram?

Distance from origin to the point

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

z=a2+b2|z| = \sqrt{a^2 + b^2}

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

55

What does the argument arg(z)\arg(z) of a complex number represent?

Angle with positive real axis

In what units is the argument of a complex number measured?

Radians

What is the formula for finding the argument of z=a+biz = a + bi?

θ=tan1(ba)\theta = \tan^{-1}\left(\frac{b}{a}\right)

On an Argand diagram, what does the xx-axis represent?

Real part of complex number

What is the polar form of a complex number?

z=z(cosθ+isinθ)z = |z|(\cos \theta + i \sin \theta)

For a complex number in Quadrant II, how is the argument adjusted?

πθ\pi - |\theta|

What is the argument of z=1+iz = 1 + i?

π4\frac{\pi}{4} radians

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