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The point A,B,C and D represent the complex number Z1,Z2,Z3 and Z4 and O is the origin. If OABC is a parallelogram, and Z1=1+3i and Z2=4+5i, find Z3

Sagot :

MrRoyal

Complex numbers are divided into two parts; real and imaginary parts. The value of Z3 is [tex]5+ 8i[/tex]

Given that:

[tex]Z_1 = 1 + 3i[/tex]

[tex]Z_2 = 4 + 5i[/tex]

Since O is the origin, then:

[tex]C = OA + OB[/tex]

This means that:

[tex]Z_3 = Z_1 + Z_2[/tex]

So, we have:

[tex]Z_3 = 1 + 3i + 4 + 5i[/tex]

Collect like terms

[tex]Z_3 = 1 + 4+ 3i + 5i[/tex]

[tex]Z_3 = 5+ 8i[/tex]

Hence, complex number Z3 is [tex]5+ 8i[/tex]

Read more about complex numbers at:

https://brainly.com/question/18509723

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