Find the magnitude of the complex number (z = 3 cos(theta) + 3i sin(theta)) where (theta = frac{pi}{4}).

Question

Accepted Answer

Step:1 ：First, we substitute (theta = frac{pi}{4}) into the complex number, so (z = 3 cosleft(frac{pi}{4}right) + 3i sinleft(frac{pi}{4}right) = 3 cdot frac{sqrt{2}}{2} + 3i cdot frac{sqrt{2}}{2} = frac{3sqrt{2}}{2} + frac{3sqrt{2}}{2}i).Step:2 ：Next, we calculate the magnitude of the complex number using the formula (|z| = sqrt{Re(z)^2 + Im(z)^2}), where Re(z) is the real part of z and Im(z) is the imaginary part of z. So, (|z| = sqrt{left(frac{3sqrt{2}}{2}right)^2 + left(frac{3sqrt{2}}{2}right)^2} = sqrt{frac{18}{2} + frac{18}{2}} = sqrt{18} = 3sqrt{2}).

Answer

Step: 1 ：First, we substitute (theta = frac{pi}{4}) into the complex number, so (z = 3 cosleft(frac{pi}{4}right) + 3i sinleft(frac{pi}{4}right) = 3 cdot frac{sqrt{2}}{2} + 3i cdot frac{sqrt{2}}{2} = frac{3sqrt{2}}{2} + frac{3sqrt{2}}{2}i).Step: 2 ：Next, we calculate the magnitude of the complex number using the formula (|z| = sqrt{Re(z)^2 + Im(z)^2}), where Re(z) is the real part of z and Im(z) is the imaginary part of z. So, (|z| = sqrt{left(frac{3sqrt{2}}{2}right)^2 + left(frac{3sqrt{2}}{2}right)^2} = sqrt{frac{18}{2} + frac{18}{2}} = sqrt{18} = 3sqrt{2}).

Find the magnitude of the complex number $z = 3 \cos (θ) + 3 i \sin (θ)$ where $θ = \frac{π}{4}$ .

Answer

Popular Problems

Find the magnitude of the complex number z=3cos⁡(θ)+3isin⁡(θ) where θ=π4.

Answer

Popular Problems

Find the magnitude of the complex number $z = 3 \cos (θ) + 3 i \sin (θ)$ where $θ = \frac{π}{4}$ .