Question

Z1=2(cos30+i sin30) Z2=1/2(cos10+i sin10) Z1×z2 z1÷z2 z1^2 Help please

Answer 1

Відповідь:

1)2cos(30)+sin (30)cos(10)+sin(30)

2)2cos(30)+ 4 sin(30)/cos(10)+sin(10)

Покрокове пояснення:

z1=2cos(30)+2sin(30)

z2= cos(10)+sin(10)/2

z1 *z2 = 2cos(30)+2sin(30) * cos(10)+sin(10)/2=2cos(30)+sin (30)cos(10)+sin(30)

z2=2cos(30)+2sin(30) : cos(10)+sin(10)/2 =2cos(30)+ 4 sin(30)/cos(10)+sin(10)

Answer 2

Sure, I can help you with that! It looks like you're working with complex numbers and performing various operations on them. Let's go through each of the operations step by step:

Given complex numbers: Z1 = 2(cos30° + i sin30°) Z2 = 1/2(cos10° + i sin10°)

1. Multiplying Z1 and Z2 (Z1 × Z2):

To multiply two complex numbers, you can multiply their magnitudes and add their angles.

Z1 × Z2 = (2 × 1/2) (cos(30° + 10°) + i sin(30° + 10°)) = 1 (cos40° + i sin40°)

So, Z1 × Z2 = cos40° + i sin40°.

2. Dividing Z1 by Z2 (Z1 ÷ Z2):

To divide two complex numbers, you can divide their magnitudes and subtract their angles.

Z1 ÷ Z2 = (2 / 1/2) (cos(30° - 10°) + i sin(30° - 10°)) = 4 (cos20° + i sin20°)

So, Z1 ÷ Z2 = 4cos20° + 4i sin20°.

3. Squaring Z1 (Z1^2):

To square a complex number, you can square its magnitude and double its angle.

Z1^2 = (2^2) (cos(2 × 30°) + i sin(2 × 30°)) = 4 (cos60° + i sin60°) = 4 (1/2 + i √3/2) = 2 + 2i√3

So, Z1^2 = 2 + 2i√3.

To summarize:

• Z1 × Z2 = cos40° + i sin40°
• Z1 ÷ Z2 = 4cos20° + 4i sin20°
• Z1^2 = 2 + 2i√3

Keep in mind that angles are often given in degrees, and trigonometric functions like cosine and sine operate on radians. If you need results in radians, make sure to convert the angles accordingly.