Question

REALLY NEED HELP!!! see picture*****

Answer 1

Answer:

11) $r=4$

12) $z_3+z_1=A$

13a) $\bar z_1=3-2i$ and $\bar z_2=-5+3i$

13b)  $\bar {z_1z_2}=-9-19i$

Step-by-step explanation:

11. The given equation in rectangular coordinates is $x^2+y^2=16$

To convert to polar form, use the relation $x^2+y^2=r^2$

This implies that:

$\implies r^2=16$

$r=\sqrt{16}$

$r=4$

In polar coordinates, $r=4$ is a circle with radius 4 units.

12.  From the diagram;

$z_3=-3-3i$

$z_2=1+i$

$z_1=4+i$

$A=1-2i$

We can see that two arrows are moving in anticlockwise direction to meet A which is moving in the clockwise direction;

$\implies (-3-3i)+(4+i)=1-2i$

$\therefore z_3+z_1=A$

13. The conjugate of the complex number: $z=a+bi$ is $\bar z=a-bi$

Part a) The given complex numbers are:

$z_1=3+2i$ and $z_2=-5-3i$

The conjugates of these complex numbers are:

$\bar z_1=3-2i$ and $\bar z_2=-5+3i$

Part b) The product of $z_1=3+2i$ and $z_2=-5-3i$ is

$z_1z_2=(3+2i)(-5-3i)$

$z_1z_2=-15-9i-10i-6i^2$

$z_1z_2=-9-19i$

The conjugate of the product is:

$\bar {z_1z_2}=-9-19i$