DeanGD20idn
Answered

Sumali sa IDNStudy.com at makuha ang mabilis at kaugnay na mga sagot. Magtanong at makakuha ng detalyadong sagot mula sa aming komunidad ng mga eksperto na may kaalaman.

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! :))

Sagot :

PaullyMacidn

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

#CarryOnLearning

Maraming salamat sa iyong aktibong pakikilahok. Patuloy na magbahagi ng impormasyon at kasagutan. Sama-sama tayong lumikha ng isang masiglang komunidad ng pagkatuto. Salamat sa pagbisita sa IDNStudy.com. Nandito kami upang magbigay ng malinaw at tumpak na mga sagot.