calculate the following complex numbers

Question

(2+i)+(4+i)=

(2+i)-(4+i)=

(2+i)(4+i)=

(2+i)/(4+i)=

if z=2+i then ‾z=

if z=2+i then |z|=

Answer 1

Daiia,

 

6+2i add real and imaginary parts

-2

7+6i  (2x4 + 2*i+i*4+i*i)

9/17 +2i/17 ( multiply numerator and denominator by (4-i) then simplify)

don't understand the notation is it z^-1 ? if so then the answer is 2/5 -i/5

(2^2 +1^2)^1/2 = √5 (|z|=(Re(z)^2 + Im(z)^2)^1/2 )

 

Hope this helps

Jim

Answer 2

Do not place  = when you right the problems in row.

 

( 2 + i ) + ( 4 + i) = 6 + 2i

 

( 2 + i ) - ( 4 + i ) = 6

 

( 2 + i) ( 4 + i) = 8 + 4i + 2i - i^2 = 8 - ( -1 ) + 6i = 9 + 6 i

                     

if Z = 2 +i    Z = 2 - i

 

 

if  Z = 2 + i    l Z l = √( 2^2 + 1^2) = √5