Complex numbers

Question

Question 1

 

Question 2 (Really confused with this question)

 

Question 3

 

 

Answer 1

(3a)

Multiply numerator and denominater with conjugate of 1+ 2i

The complex conjugate of 1+ 2i  is 1 - 2i 

Rectangular form is  1 + 3i

Answer 2

(1)

Two points located in complex plane , they are 5 - 3i , 5

As points, the complex numbers are (5,-3) and (5,0) .

The distance formula .

So the distance between 5 - 3i and 5 is 3

Answer 3

(3b)

Multiply numerator and denominator with conjugate of 2 - i

The complex conjugate of 2 - i  is 2 + i

Rectangular form is  -1 + 2i

 

Answer 4

(3c)

Multiply numerator and denominator with conjugate of -1+4i

The complex conjugate of 2 - i  is -1-4i

Rectangular form is  1 + 2i