Write each quotient as a complex number. $\frac{4-3i}{-1-4i}$

Elma Wilson
2021-12-04
Answered

Write each quotient as a complex number. $\frac{4-3i}{-1-4i}$

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Daniel Williams

Answered 2021-12-05
Author has **14** answers

Write each quotient as a complex number

$\frac{4-3i}{-1-4i}$

Key concept: you can use complex conjugates to simplify quotients of complex numbers.

$\frac{4-3i}{-1-4i}\cdot (-1+4i)$

Rewrite the quotient so you are able to distribute

$\frac{(-1+4i)(4-3i)}{(-1+4i)(-1-4i)}$

Distribute

$\frac{-4+3i+16i-12{i}^{2}}{1+4i-4i-{16}^{2}}$

Key Concept:${i}^{2}-1$

$\frac{-4+3i+16i-12(-1)}{1+4i-4i-16(-1)}$

Simplify the equation

$\frac{8+19i}{17}$

Simplify so the real part is apart from the imaginary part

$\frac{8}{17}+\frac{19i}{17}$

Result:

$\frac{8}{17}+\frac{19i}{17}$

Key concept: you can use complex conjugates to simplify quotients of complex numbers.

Rewrite the quotient so you are able to distribute

Distribute

Key Concept:

Simplify the equation

Simplify so the real part is apart from the imaginary part

Result:

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