Perform each of the following operations. Make sure to write your answers as complex numbers.

Question

a) (2−5𝑖)^2

b) 7−2𝑖 /1+4𝑖

Answer 1

(2-5i) (2-5i) = 2.2 - 10i - 10i + 25i² = 4 - 20i -25 = -21 - 20i

7-2i / 1 + 4i

To get a real number in the denominator multiply top and bottom by conjugate of denominator ie 1 - 4i

(7-2i) ( 1-4i) / (1+4i) (1-4i) = (7 - 28i - 2i + 8i² ) / (1 - 4i + 4i - 16i²) = (-1 - 30i) / (17) = (-1/17) - (30/17) i