Perform the operations of the complex numbers Write the answ

Perform the operations of the complex numbers. Write the answers in standard form of a complex number a+bi. (6 + 5i) - (3 - i) = (5 - 8i)^2 = 3 + 8i/1 + 3i =

Solution

a) (6 +5i) - ( 3- i) = 6 +5i -3 +i = 3 +6i

b) (5 - 8i)^2 = 5^2 + (8i)^2 - 2*5*(8i)

= 25 - 64 - 80i

= -39 - 80i

c) ( 3+8i)/(1+3i)

Rationalise denominator by multiplying with conjugate with num. and den.

(3+8i)(1-3i)/(1+9)

( 3 - 9i +8i +24)/10

27/10 - i/10

2.7 - 0.1*i