DeanGD20viz
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Adam starts with the number z = 1 + 2i on the complex plane. First, he dilates z by a factor of 2 about the origin. Then, he reflects it across the real axis. Finally, he rotates it 90° counterclockwise about the origin. The resulting complex number can be written in the form a + bi where a and b are real numbers. What is the resulting complex number?

Please answer with solution, thanks in advance! :))

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PaullyMacviz

Answer:

4 + 2i

Step-by-step explanation:

Given: The starting number is z = 1 + 2i.

After getting dilated by a factor of 2, z becomes 2 + 4i

.

Then, the number is reflected across the real axis, so the number becomes  2 - 4i

.

Now, the resulting number (2 - 4i) is rotated 90° anticlockwise.

We know that if the point (a, b) is rotated anticlockwise by the angle α, then we get point  (a cos α − b sin α, b cos α + a sin α).

So (2, -4) after getting rotated by 90° anticlockwise becomes  (2 cos 90° + 4 sin 90°, −4 cos 90° + 2 sin 90°) = (4, 2).

So, the resulting complex number is 4 + 2i

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