Write the expression in the form that abi where a and b are

Write the expression in the form that a+bi, where a and b are real numbers

Write the expression (8- 5t) + (-4+ 8i)

a. (8 -5i) + ( -4 +8i)

adding real parts together and imaginary parts:

( 8-4) +( -5i +8i) = 4 +3i

b. ( 1+5i)(1-2i )

Multiplying the terms inside the brackets:

1 -2i + 5i -10i*i

= 1 +3i +10 = 11 +3i

c. ( 8-5i)^2

Expand using the formula : (a +b)^2 = a^2 +b^2 +2ab

( 8-5i)^2 = 64 - 25 -80i = 40 - 80i

d. i( 6 + 5i)^2

Exapnd using the formula above : i( 36 -25 + 60i)

= 36i -25i -60

= -60 - 61i

f. i^29 = i*i^28 = i(i^2)^14

i*i = -1

i^29 = i*i^28 = i(i^2)^14 = i(-1)^14 = i