Simplify the following expression below:

1 answer:

7 0

So, 4/3 - 2i

4/3 - 2i = 12/13 + i8/13

multiply by the conjugate:
3 + 2i/3 + 2i
= 4(3 + 2i)/(3 - 2i) (3 + 2i)
(3 - 2i) (3 + 2i) = 13

(3 - 2i) (3 + 2i)

apply complex arithmetic rule: (a + bi) (a - bi) = a^2 + b^2
a = 3, b = - 2
= 3^2 + (- 2)^2

refine: = 13
= 4(3 + 2i)/13

distribute parentheses:
a(b + c) = ab + ac
a = 4, b = 3, c = 2i
= 4(3) + 4(2i)

Simplify:
4(3) + 4(2i)
12 + 8i

4(3) + 4(2i)
Multiply the numbers: 4(3) = 12
= 12 + 2(4i)

Multiply the numbers: 4(2) = 8
= 12 + 8i

12 + 8i
= 12 + 8i/13

Group the real par, and the imaginary part of the complex numbers:

Your answer is: 12/13 + 8i/13

Hope that helps!!!

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