Chapter A.7, Problem 8AYU

To determine

To find: Whether the statement is true or false.

Answer to Problem 8AYU

The statement is false.

Explanation of Solution

Given information:

The given statement is “If $2-3i$ is a solution of quadratic equation with real coefficients, then $-2+3i$ is also a solution”.

Calculation:

The standard form a complex number is $a+ib$ .

The conjugate of complex number is obtained by adding a minus sign before the imaginary part.

The conjugate is thus expressed as,

$a-ib$ .

A quadratic number has two solutions and if the root of a quadratic equation is complex then its other root will be conjugate.

If one solution is $2-3i$ then the other solution will be $2+3i$ .

Therefore, the given statement is false.