Transformations (Leaving Cert Mathematics): Quizzes

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Transformations
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In the complex plane, what does the real part of a complex number represent?

The xx-coordinate

In the complex plane, what does the imaginary part represent?

The yy-coordinate

If z1=2−3iz_1=2-3i and z2=1+2iz_2=1+2i, by how many units does adding z2z_2 shift z1z_1 in real component?

1 unit to the right

If z1=2−3iz_1=2-3i and z2=1+2iz_2=1+2i, how many units does adding z2z_2 shift z1z_1 in imaginary axis?

2 units

What does multiplying a complex number by a scalar constant kk do to its magnitude?

Expands or compresses it

If z1=2+3iz_1=2+3i, what happens to the magnitude when calculating 2z12z_1?

It doubles

What transformation does the conjugate of a complex number perform?

Flip across real axis

Across which axis does the conjugate reflect a complex number?

The real axis

What happens when you multiply a complex number by ii?

Rotates 90°90° anticlockwise

What rotation occurs when multiplying a complex number by −i-i?

90°90° clockwise

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