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

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Modulus-Argument Form
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What is the modulus-argument form also known as?

Polar form

In z=r(cos⁡θ+isin⁡θ)z = r(\cos \theta + i \sin \theta), what does rr represent?

The modulus of zz

In modulus-argument form, what does θ\theta represent?

The argument of zz

What does 'cis' stand for in the notation z=r cis θz = r \text{ cis } \theta?

cos⁡θ+isin⁡θ\cos \theta + i \sin \theta

For z=a+biz = a + bi, what is the formula for the modulus rr?

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

For z=a+biz = a + bi, what is the initial formula for the argument θ\theta?

θ=tan⁡−1(ba)\theta = \tan^{-1}(\frac{b}{a})

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

2\sqrt{2}

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

55

When multiplying z1×z2z_1 \times z_2, how are the arguments combined?

θ1+θ2\theta_1 + \theta_2

When dividing z1z2\frac{z_1}{z_2}, how are the moduli combined?

r1r2\frac{r_1}{r_2}

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