NDA MATHEMATICS QUIZ - 2

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Question 1:

If $a+i b=\left(\frac{1+i}{1-i^{2}}\right)^{200}$ then:

Question 2:

Argument of the number $z=-1+\sqrt{3}i$ is:

Question 3:

If $\alpha$ be the cube root of unity then $1+\alpha+\alpha^{2}+\cdots+\alpha^{n-1}$ equals:

Question 4:

If $(3 a-2 i b)(2+i)^{2}=10(1+i)$ then value of $(a$, b) will be:

Question 5:

If $z_{1}$ and $z_{2}$ be two complex numbers where $z_{1}=-2+4 i$ and $z_{2}=1-i$ then $\operatorname{Re}\left(\frac{z_{1} z_{2}}{\bar{z}_{2}}\right)$ is:

Question 6:

Multiplicative inverse of $(4+3 i)$ will be

Question 7:

If $\frac{3}{\cos \theta+i \sin \theta+2}=a+i b$ then $a^{2}+b^{2}-4 a$ equals:

Question 8:

Value of $i^{n}+i^{n+1}+i^{n+2}+i^{n+3}$ is equal to:

Question 9:

The quadratic equation whose one root is a square root $-47+8 \sqrt{-3}$; will be:

Question 10:

If $\left|z-\frac{4}{z}\right|=2$ then $|z|$ cannot be less than: