# Write all of the complex numbers that are graphed in the complex plane shown. A: _ + _i, B: _ + _i, C: _ + _i, D: _ + _i

A complex number is the sum of a real number and an imaginary number and it is represented as x + iy, where x, y are real numbers. A complex number is usually denoted by z.

## Answer: The complex numbers that are graphed in the complex plane shown are, A: -2 + 3i, B: -1 - 1i, C: 3 - 4i, D: 4 + 1i

Let's look into the solution below.

**Explanation:**

A complex number is represented as z = x + iy. Here, both x and y are real numbers.

- x is called the real part which is denoted by Re(z).
- y is called the imaginary part which is denoted by Im(z).
- i is an imaginary number.

Based on the definition we will look into the x and y coordinates of each of the points A, B, C, and D showed in the graph.

Let's look into the coordinates (x,y) of each of these points along with their representation in complex form.

Coordinates of the Points (x,y) | Complex Number Representation = x + iy |

A(-2, 3) | -2 + 3i |

B(-1, -1) | -1 - 1i |

C(3, -4) | 3 - 4i |

D(4, 1) | 4 + 1i |

We can use Cuemath's Online complex numbers calculator to perform different arithmetic operations on complex numbers.

### Thus, we have represented the given points A: -2 + 3i, B: -1 - 1i, C: 3 - 4i, D: 4 + 1i in their complex form.

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