Class XI

Solving Equations with Complex Solutions

Lesson

Practice

Lesson

Worked Examples

Question 1

Find all the complex solutions of $x^2=-4$x2=−4.

Write all the solutions in the form $a+ib$a+ib on the same line, separating each one with a comma.

Question 2

Find all the complex solutions of $x^3+64=0$x3+64=0.

Write all the solutions in the form $a+ib$a+ib on the same line, separating each one with a comma.

Question 3

Find the complex solutions of $x^4-81i=0$x4−81i=0.

Write all the solutions in trigonometric form (with arguments in degrees) on the same line, separating each one with a comma.

Outcomes

11.A.CNQE.1

Need for complex numbers, especially √-1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.