Solveeit Logo
Login

Question

Question: The modulus and amplitude of \(\frac{\pi}{2} + \frac{\alpha}{2}\) are....

The modulus and amplitude of π2+α2\frac{\pi}{2} + \frac{\alpha}{2} are.

A

π2−α2\frac{\pi}{2} - \frac{\alpha}{2}

B

1 and 0

C

1 and z1,z2∈Cz_{1},z_{2} \in C

D

1 and amp(z1zˉ2)=amp\left( \frac{z_{1}}{{\bar{z}}_{2}} \right) =

Answer

1 and 0

Explanation

Solution

1+7i(2−i)2=(1+7i)(3−4i)(3+4i)(3+4i)=−25+25i25=−1+i\frac{1 + 7i}{(2 - i)^{2}} = \frac{(1 + 7i)}{(3 - 4i)}\frac{(3 + 4i)}{(3 + 4i)} = \frac{- 25 + 25i}{25} = - 1 + i

Modulus =1

Amplitude z=x+iy=−1+iz = x + iy = - 1 + i =∴rcos⁡θ=−1\therefore r\cos\theta = - 1