Question

11 POINTS PLZ HELP EMERGENCY

Answer 1

Part A

The given expression is:

$(-5(1+2i)+3i(3-4i)$

We expand to get:

$-5-10i+9i-12i^2$

Note that $i^2=-1$

$12-5-10i+9i$

$-5-10i+9i+12$

$7-i$

Part Bi)

The given expression is;

$\sqrt{-50}$

We simplify to get:

$\sqrt{25\times 2\times -1}$

$\sqrt{25\times} \sqr{2}\times \sqrt{-1}$

Note that:

$\sqrt{-1}=i$

$5\sqr{2}i$

This is now of the form $a+bi$, where $a=0,b=5\sqr{2}$.

This explains why it is a complex number;

Part bii)

The given expression is :

$\frac{\sqrt{-50} }{\sqrt{5}}$

We simplify to get

$\sqrt{\frac{-50 }{5}}$

$\sqrt{-25}$

$\sqrt{-25}=\sqrt{25}\times \sqrt{-1}$

$\sqrt{-25}=5\times i$

$\sqrt{-25}=5i$

Part C

We want to simplify:

$i^{22}$

We rewrite in terms of $i^2$

$i^{22}=(i^2)^{11}$

$i^{22}=(-1)^{11}$

$i^{22}=-11$