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Question

Question: If \(- \frac{\pi}{2}\) then \(z\) is equal to....

If −π2- \frac{\pi}{2} then zz is equal to.

A

zz

B

−iz- iz

C

π\pi

D

−π2- \frac{\pi}{2}

Answer

zz

Explanation

Solution

Since arg =cos⁡(α+β−γ−δ)+isin⁡(α+β−γ−δ)= \cos(\alpha + \beta - \gamma - \delta) + i\sin(\alpha + \beta - \gamma - \delta) i.e. – ve, we choose arg z = – θ

where (cos⁡α+isin⁡α)(cos⁡β+isin⁡β)(cos⁡γ+isin⁡γ)(cos⁡δ+isin⁡δ)\frac{(\cos\alpha + i\sin\alpha)(\cos\beta + i\sin\beta)}{(\cos\gamma + i\sin\gamma)(\cos\delta + i\sin\delta)} is cos⁡n(π2−θ)+isin⁡n(π2−θ)\cos n\left( \frac{\pi}{2} - \theta \right) + i\sin n\left( \frac{\pi}{2} - \theta \right)arg

2xy=−62xy = - 6

x2+y2=64+36=±10x^{2} + y^{2} = \sqrt{64 + 36} = \pm 10

x=±1x = \pm 1