Question

HELP! Find the product of z1=5(cos 20 degrees+ i sin 20 degrees) and z2=4(cos 10 degrees + i sin 10 degrees) and write the answer in standard form.

Answer 1

i really need help fast

Answer 2

Hint:

If z1 = r1*cis(theta1) and z2 = r2*cis(theta2)

Then

z1*z2 = (r1*r2)*cis(theta1+theta2)

Answer 3

great, just convert them into euler's form, that is:
\(re^{i\theta} = r(\cos \theta + \iota \sin \theta)\)

And then multiply both the complex nos. this should be the easiest method.

Answer 4

can you show me?please

Answer 5

In z1=5(cos 20 degrees+ i sin 20 degrees) , what is r and theta?

Answer 6

well, your two nos. are:
\(z_1 = 5(\cos 20^0 + \iota \sin 20^0) = 5 e^{i 20^o}\)

Similarly what would \(z_2\) be?

Answer 7

is it 6.4

Answer 8

Can u help

Answer 9

Not sure how you're getting 6.4

Answer 10

I solved that equation? can u walk through please? i did it wrong

Answer 11

In z1=5(cos 20 degrees+ i sin 20 degrees), r1 is 5 and theta1 is 20

In z2=4(cos 10 degrees + i sin 10 degrees), r2 is 4 and theta2 is 10

So

z1*z2 = (r1*r2)*cis(theta1+theta2)

z1*z2 = (5*4)*cis(20+10)

z1*z2 = 20*cis(30)

z1*z2 = 20*( cos(30) + i*sin(30) )

z1*z2 = 20*( sqrt(3)/2 + i*(1/2) )

z1*z2 = 20*( sqrt(3)/2) +20*( i*(1/2) )

z1*z2 = 10*sqrt(3) + 10i

Answer 12

The first part is just recognizing/remembering the formula. The remaining parts involve simplifying really.