Math Count Level 3

 $z_{1\ }and\ z_2\$  are complex numbers, where
 $z_1=1+i\ ,\ z_2=-2-2i$  
What is  $z_1+z_2$  in cartesian form?

•  $\sqrt{10}$  

•  $-1-i$  

•  $3-i$  

•  $-1+3i$  

 $z$  is a complex number, where
 $z=1+\sqrt{6}i$  
What is the modulus of z?

•  $\sqrt{7}$  

•   $67.79\degree$  

•  $7$   

•  $\sqrt{1+\sqrt{6}}$  
  

What is the value of  $i^{2003}$  when   $i=\sqrt{-1}$  ?

•  $i$  

•  $-i$  

•  $1$  

•  $-1$  

 $z_{1\ }and\ z_2\$  are complex numbers, where
 $z_1=1+i\ ,\ z_2=-2-2i$  
What is the value of  $\frac{z_1}{z_2}$  in polar form?

•  $\frac{1}{2}\left[\cos\left(\frac{\pi}{2}\right)+i\ \sin\left(\frac{\pi}{2}\right)\right]$  
  

•  $\frac{1}{2}\left[\cos\left(\frac{\pi}{3}\right)+i\ \sin\left(\frac{\pi}{3}\right)\right]$  
  

•  $\left[\cos\left(\frac{\pi}{2}\right)+i\ \sin\left(\frac{\pi}{2}\right)\right]$  
  

•  $\frac{1}{2}\left[\cos\left(\pi\right)+i\ \sin\left(\pi\right)\right]$  
  

Find the range of x, where  $\frac{x^2}{(x-14)}<-1$  .

•  $\left(-∞,\frac{-1+\sqrt{57}}{2}\right)\cup\left(\frac{-1+\sqrt{57}}{2},14\right)$  

•  $\left(-∞,\frac{-1-\sqrt{57}}{2}\right)\cup\left(\frac{\sqrt{57}-1}{2},14\right)$  

•  $\left(-∞,\frac{-1-\sqrt{46}}{2}\right)\cup\left(\frac{\sqrt{57}-1}{2},14\right)$  

•  $\left(-∞,\frac{-1+\sqrt{46}}{2}\right)\cup\left(\frac{\sqrt{57}-1}{2},14\right)$  

Find the number of the multiples of 8 between 100 and 300.

• 29

• 25

• 23

• 21

The third and eight terms of an arithmethic sequence are -5 and 15 respectively, Find the first term.

• -13

• -7

• 13

• 7

 $\frac{2\ }{3},\frac{2}{9}\ ,\frac{2}{27},\ …$  
Find the sum to infinity of the geometric sequence above.

•  $1$  

•  $\frac{2}{3}$  

•  $\frac{4}{3}$  

•  $\frac{5}{3}$  

De morgan’s theorem in theory of set states that  $(A\cup B)'$  is equivalent to

•  $A’∩B’$  

•  $\left(A\cap B\right)'$  

•  $A’\cup B’$  

 $f(b)=4b^2-3b+2$  is a function with complex roots. Hence, find the roots.

•  $\frac{3-i\sqrt{23}}{8}\ ,\ \frac{3+i\sqrt{23}}{8}$  

•  $\frac{3-i\sqrt{23}}{4}\ ,\ \frac{3+i\sqrt{23}}{4}$  

•  $\frac{\sqrt{23}-3i}{8}\ ,\ \frac{\sqrt{23}+3i}{8}$  

•  $\frac{\sqrt{23}-3i}{4}\ ,\ \frac{\sqrt{23}+3i}{4}$