Answered: Find the exact solutions to the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section: Chapter Questions

Problem 7T

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Question

Find the exact solutions to the equations in the complex numbers.

z²-4z+6=0

Expert Solution

Step 1

Given equation is,

z²-4z+6=0

Comparing the above equation with standard quadratic equation,

$a x^{2} + b x + c = 0$

The solution to the above equation is,

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Step 2

Calculating the solution for the above equation,

$z = \frac{- (- 4) \pm \sqrt{{(- 4)}^{2} - 4 \times 1 \times 6}}{2 \times 1} z = \frac{4 \pm \sqrt{16 - 24}}{2} z = \frac{4 \pm \sqrt{- 8}}{2} z = \frac{4 \pm \sqrt{8} \sqrt{- 1}}{2}$

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