What are pure imaginary numbers with examples?

Pure imaginary numbers The number i is by no means alone! For example, 3 i 3i 3i , i 5 i\sqrt{5} i5 ​i, square root of, 5, end square root, and −12i are all examples of pure imaginary numbers, or numbers of the form b i bi bi , where b is a nonzero real number.

How do you know if a number is purely imaginary?

If z≠0, this means that z is purely imaginary. There is also a nice geometric interpretation: |z−1| is the distance from z to 1, and |z+1| is the distance to −1. If these are equal, then z must lie on the perpendicular bisector of the line segment connecting 1 and −1, which is the line x=0.

Is 5i a pure imaginary number?

The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. By definition, zero is considered to be both real and imaginary.

Is 0 a pure imaginary number?

a is said to be the real part of z. b is said to be the imaginary part of z. z is said to be a purely imaginary number if its real part is equal to 0. Hence, 0 is a purely imaginary number because its real part is 0.

What is 4i?

So, the square root of -16 is 4i. All negative square roots are called “imaginary numbers” (now you know where that letter ‘i’ comes from). Complex Numbers. When a number has the form a + bi (a real number plus an imaginary number) it is called a “complex number”.

What is the difference between imaginary numbers and complex numbers?

A complex number is the sum of a real number and an imaginary number. A complex number is expressed in standard form when written a + bi where a is the real part and bi is the imaginary part. Imaginary numbers are distinguished from real numbers because a squared imaginary number produces a negative real number.

What is the difference between pure imaginary number and imaginary number?

What is purely real and purely imaginary?

A complex number z is said to be: Purely real, if Im(z) = 0, Purely imaginary, if Re(z) = 0.

Is Pi an imaginary number?

No. Pi is an irrational transcendental real number.

Is 0i a complex number?

A real number is a complex number whose imaginary part is 0. The imaginary part of 0 + 0i is 0, and therefore it is a real number. It seems preferential to real numbers in the complex plane. It would make perfect sense to me to classify 0 as non-real.

Is 24i a real number?

The real part of 24i is 0. The real part of 24i is 0.