Can a complex number be equal to zero?

Zero: To equal zero, a complex number must have both its real part and its imaginary part equal to zero: a + bi = 0 if and only if a = 0 and b = 0.

How do you know if complex numbers are equal?

The Complex Plane a is called the real part of the complex number, and b is called the imaginary part. Two complex numbers are equal if and only if their real parts are equal and their imaginary parts are equal. I.e., a+bi = c+di if and only if a = c, and b = d.

Is a complex no or not?

A complex number is a number of the form a + bi, where a and b are real numbers, and i is an indeterminate satisfying i2 = −1. For example, 2 + 3i is a complex number. To emphasize, the imaginary part does not include a factor i; that is, the imaginary part is b, not bi.

Is z a complex number?

z, a number in the complex plane The imaginary number i is defined as: When an imaginary number (ib) is combined with a real number (a), the result is a complex number, z: The real part of z is denoted as Re(z) = a and the imaginary part is Im(z) = b.

What is the value of ZW if two complex numbers are equal?

Now, if two complex numbers are equal, then their real parts have to be equal and their imaginary parts have to be equal. In order that zw = 1, we’ll need ( xu – yv ) + ( xv + yu) i = 1.

How do you divide z by a non-zero complex number?

The division of a complex number z by a non-zero complex number z1 can be represented as z/z1. We can also multiply z with the multiplicative inverse of z1. It can also be represented as z/z1. Let z = a + ib and z1 = a1 + ib1.

What is the set C of complex numbers?

1 Review of complex numbers. 1.1 Complex numbers: algebra. The set C of complex numbers is formed by adding a square root iof 1 to the set of real numbers: i2 = 1. Every complex number can be written uniquely as a+bi, where aand bare real numbers.

How do you find 1/ z given Z?

So we set ourselves the problem of finding 1/ z given z. In other words, given a complex number z = x + yi, find another complex number w = u + vi such that zw = 1. By now, we can do that both algebraically and geometrically.