Question

You know 4−3i is the complex conjugate of 4+3i. If you multiply the denominator of −2+5i4+3i by 4−3i, what will you get? Enter your answer as a number, like this: 42 Algebra 2

Answer 1

25

Explanation:

Given

(-2 + 5i)/(4 + 3i)

Required

Multiply the denominator by 4 - 3i

The denominator of the fraction above is 4 + 3i

When multiplied by 4 - 3i, the result is as follows;.

Result = (4 + 3i)(4 - 3i)

Expand

Result = 4(4 - 3i) + 3i(4 - 3i)

Open both brackets (take it one at a time)

Result = 4 * 4 - 4 * 3i + 3i(4 - 3i)

Result = 16 - 12i + 3i(4 - 3i)

Open the second bracket

Result = 16 - 12i + 12i - 3i * 3i

Result = 16 - 12i + 12i - 9i²

In complex numbers, i = √-1

i² = (√-1)²

i² = √-1 * √-1

i² = -1

The expression

Result = 16 - 12i + 12i - 9i²

Becomes

Result = 16 - 12i + 12i - 9(-1)

Result = 16 - 12i + 12i + 9

Collect like terms

Result = 16 + 9 + 12i - 12i

Result = 25 + 0

Result = 25

Hence, when the denominator of the fraction is multiplied by 4 - 3i, the result is 25