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Consider the complex number on the complex plane and the complex number z2 = 6 – 3i.


On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. Point Z 1 is (2, 1).


When z1 and z2 are added together, the result moves z1 6 units ____

and 3 units

.


The real part of z1 + z2 is ____

.


The imaginary part of z1 + z2 is ____

i.

Consider The Complex Number On The Complex Plane And The Complex Number Z2 6 3iOn A Coordinate Plane The Yaxis Is Labeled Imaginary And The Xaxis Is Labeled Rea class=

Sagot :

When z1 and z2 are added together, the result moves z1 6 units right

and 3 units down.

The real part of z1 + z2 is 8.

The imaginary part of z1 + z2 is –2i.

Anuksha0456idn

When z1 and z2 are added together, the result moves z1 6 units right and 3 units down.

The real part of z1 + z2 is 8.

The imaginary part of z1 + z2 is -2.

What are complex numbers?

A complex number is of the form a + bi, a, b are Real numbers, and i = √(-1). It is used to determine the values of square roots of negative numbers. It is represented in the coordinate plane with the real part on the x-axis and imaginary part b on the y-axis, the ordered pair being (a, b).

How do we solve the given question?

In the question, we are given two complex numbers,

z1 = 2 + i

z2 = 6 - 3i

These points are represented on the Coordinate plane as a circle and a triangle respectively. We calculate their sum, z3.

To add Complex Numbers, the real parts are added to the real parts and the imaginary to the imaginary.

∴ z3 = z1 + z2 = (2 + i) + (6 - 3i) = (2+6) + (1-3)i = 8 -2i.

This point is represented as a square on the Coordinate plane.

By observing the coordinate plane, we can say that:

When z1 and z2 are added together, the result moves z1 6 units right and 3 units down.

Observing z3, we can tell that its real part is 8, and its imaginary part is -2.

∴ The real part of z1 + z2 is 8

∴ The imaginary part of z1 + z2 is -2

Learn more about Complex Numbers at

https://brainly.com/question/10662770

#SPJ2

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