Class XI

Square roots of Complex Numbers

Lesson

Interactive practice questions

Suppose $z=16\left(\cos40^\circ+i\sin40^\circ\right)$z=16(cos40°+isin40°).

What is the magnitude, $r$r, of any fourth root of $z$z?

What is the argument of the fourth root of $z$z with the least positive argument $\theta$θ?

Easy

1min

Consider the $ten$ th roots of $1$1.

Easy

1min

Find the square roots of $36i$36i in rectangular form.

Write all roots on the same line, separating each one with a comma.

Medium

1min

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.

Square roots of Complex Numbers

Interactive practice questions

Outcomes

11.A.CNQE.1

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