Multiply and simplify 9 4i2 Write the answer in the form a

Multiply and simplify: (9 + 4i)^2. Write the answer in the form a + bi, where a and b are real numbers.

Solution

( 9 + 4i )²

Please apply identity (a + b)² = a² + b² + 2ab in the above question, we will get:

= 9² + (4i)² + 2*9*4i

= 81 + 16i² + 72i

= 81 + 16(-1) + 72i (Since we know i² = -1)

= 81 - 16 +72i

= 65 + 72i

This is the answer on the form of a + bi where a and b are real numbers.