Math Cambridge - 11th grade

What is the sum of  $z_1=-3+4i$  and  $z_2=5i-10$  

•  $2-6i$  

•  $9i+13$  

•  $-13+9i$  

•  $i+9$  

Calculate   $i^{129}$  

Work out the value of

 $\frac{3-i}{2-2i}$  

•  $8+\frac{1}{2}i$  

•  $8+4i$  

•  $5+7i$  

•  $1+\frac{1}{2}i$  

What is the trigonometric form of
 $𝑧=−4+4𝑖$  

•  $4\left(\cos\ \frac{3\pi}{4}+i\sin\ \frac{3\pi}{4}\right)$  

•  $4\sqrt{2}\left(\cos\ \frac{3\pi}{4}+i\sin\ \frac{3\pi}{4}\right)$  

•  $4\sqrt{2}\left(\cos\ \frac{\pi}{4}+i\sin\ \frac{\pi}{4}\right)$  

•  $10\left(\cos\ \frac{\pi}{3}+i\sin\ \frac{3\pi}{4}\right)$  

Select the correct formula for the multiplication of complex numbers given in the trigonometric form

• $\frac{r_1}{r_2}\left[\cos\left(\theta_1-\theta_2\right)+i\sin\left(\theta_1-\theta_2\right)\right]$

• $r_1r_2\left[\cos\ \frac{\theta_1}{\theta_2}+i\sin\frac{\theta_1}{\theta_2}\right]$

• $r_1r_2\left[\cos\left(\theta_1+\theta_2\right)+i\sin\left(\theta_1+\theta_2\right)\right]$

• $\frac{r_1}{r_2}\left[\cos\left(\theta_1+\theta_2\right)+i\sin\left(\theta_1+\theta_2\right)\right]$

The green vector represents

• $\overrightarrow{a\ }\ -\overrightarrow{b\ }\$

• $\overrightarrow{a\ }\ \times\overrightarrow{b\ }\$

• $\overrightarrow{a\ }\ +\overrightarrow{b\ }\$

• $2\overrightarrow{a\ }\$

What is the magnitude of  $\overrightarrow{AB}=\left(-8,6\right)$  

Work out  $3\overrightarrow{a\ }-5\overrightarrow{b\ }$  

• (14, -16)

• (14, 4)

• (9, 4)

• (4, 4)

Select all the true options

• $\overrightarrow{a\ }+\overrightarrow{b\ }=\overrightarrow{e\ }$

• $\overrightarrow{b\ }+\overrightarrow{c\ }=\overrightarrow{a\ }$

• $\overrightarrow{c\ }+\overrightarrow{d\ }=\overrightarrow{e\ }$

• $\overrightarrow{a\ }-\overrightarrow{b\ }=\overrightarrow{c\ }$

• $\overrightarrow{d\ }+\overrightarrow{a\ }=\overrightarrow{c\ }$

What is the magnitude of  $\overrightarrow{i\ \ },\ \overrightarrow{j\ \ }and\ \overrightarrow{k\ }$  ?

• 100

• 0

• 10

• 1