Roots of Complex Numbers (Edexcel A-Level Further Mathematics): Quizzes

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Roots of Complex Numbers
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Which theorem is used to find the roots of complex numbers?

de Moivre's Theorem

How many distinct nnth roots does a complex number have?

nn distinct roots

What values does kk take when finding nnth roots?

k=0,1,2,,n1k = 0, 1, 2, \dots, n-1

In the formula for nnth roots, what does rr represent?

The modulus

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

424\sqrt{2}

What is the argument of z=4+4iz = 4 + 4i?

π4\frac{\pi}{4}

How many square roots does a complex number have?

2

Which is a cube root of 88?

1+i3-1 + i\sqrt{3}

How are nnth roots arranged on the Argand diagram?

Evenly spaced forming a regular polygon

What is the modulus of each square root of 4+4i4 + 4i?

22

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