A number that contains a real number and an imaginary number in either addition or subtraction form is called a complex number.

A complex number is a quantity and it is formed by the combination of a real number and an imaginary number. They are interconnected by either a plus sign $(+)$ or a minus $(-)$ sign to form a complex numbers mathematically.

For example, $a$ and $b$ are literals but represents real numbers. Take the imaginary number as the product of imaginary unit and $b$. A complex number is usually represented by either $a+bi$ or $a-bi$ in mathematics.

Complex numbers are formed in three different ways possibly.

01

A complex number is usually have both real and imaginary parts. A real number represents the real part of the complex number and the product of a real number and an imaginary unit represents the imaginary part of the complex numbers.

$(1) \,\,\,\,\,\,$ $3+5i$

$(2) \,\,\,\,\,\,$ $-7+4i$

$(3) \,\,\,\,\,\,$ $-9-\dfrac{4}{3}i$

$(4) \,\,\,\,\,\,$ $0.75+3i$

$(5) \,\,\,\,\,\,$ $8-\sqrt{5}i$

02

The real part of a complex number can be zero because zero is also a real number. Therefore, a complex number can only have imaginary quantity in some cases. In these types of cases, you have to assume that the real part of the complex number is zero. For example, $0+7i = 7i$

$(1) \,\,\,\,\,\,$ $2i$

$(2) \,\,\,\,\,\,$ $-5i$

$(3) \,\,\,\,\,\,$ $\dfrac{1}{7}i$

$(4) \,\,\,\,\,\,$ $-\sqrt[4]{3}i$

$(5) \,\,\,\,\,\,$ $80.9i$

03

Similarly, the imaginary part of a complex number can also be zero. In fact, an imaginary quantity is a product of imaginary unit and a real number. It is possible, an imaginary number is formed by the product of imaginary unit and zero. For example, $4-0i = 4$. Hence, every real number can be imagined as a complex number.

$(1) \,\,\,\,\,\,$ $\sqrt{6}$

$(2) \,\,\,\,\,\,$ $\dfrac{8}{9}$

$(3) \,\,\,\,\,\,$ $-0.17$

$(4) \,\,\,\,\,\,$ $3$

$(5) \,\,\,\,\,\,$ $-9$

Latest Math Topics

May 21, 2023

May 16, 2023

May 10, 2023

May 03, 2023

Latest Math Problems

May 09, 2023

A best free mathematics education website that helps students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved