Question

Express (2-3i)^2 in the form of a+bi

Answer 1

Answer:

• (2 - 3i)² = -5 - 12i

• a = -5 , b = -12

Note:

i = √(-1)

i² = -1

i³ = i²×i = -1×i = -i

i⁴ = (i²)² = (-1)² = 1

Solution:

Here,

We need to express (2 - 3i)² in the form of a + bi .

Thus,

Using the identity (A - B)² = A² - 2AB + B² ,

We have ;

=> (2 - 3i)² = 2² - 2×2×3i + (3i)²

=> (2 - 3i)² = 4 - 12i + 9i²

=> (2 - 3i)² = 4 - 12i + 9(-1)

=> (2 - 3i)² = 4 - 12i - 9

=> (2 - 3i)² = -5 - 12i

Clearly ,

-5 - 12i is in the form of a + bi , where

a = -5 and b = -12

Hence,

(2 - 3i)² = -5 - 12i

a = -5 and b = -12