Title: TTK-006 The opposite of a complex number_EN

Ilma pealkirjata Text

The Opposite of a Complex Number

Ilma pealkirjata Text

The opposite of a complex number \(z=a + bi\) is called a number \(-z\),

\(-z=-(a + bi) = -a - bi\).

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Example 1 Find the opposite of the number \(z=5+4i\;\).

Solution: \(-z=\color{red}{-}(5+4i)=-5-4i\).

Example 2 Find the opposite of the number \(z=6 - 4i\;\).

Solution: \(-z=\color{red}{-}(6 - 4i)=-6+4i\).

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Example 3 Find the opposite of the number \(z=-5+4i\).

Solution: \(-z=\color{red}{-}(-5+4i)=5-4i\).

Example 4 Find the opposite of the number \(z=-6 - 4i\).

Solution: \(-z=\color{red}{-}(-6 - 4i)=6+4i\).

Opposite Fill in the Blanks

Find the opposite of the number \(z\).

Q: 1) if \(z = 2+i\) then \(-{z}\) = [...]

2) if \(z = 1-5i\) then\(-{z}\) = [...]

3) if \(z = -2+18i\) then \(-{z}\) = [...]

4) if \(z = -3-i\) then\(-{z}\) = [...]
A: -2-i; -1+5i; 2-18i; 3+i
Feedback (0 to 100%): \(\begin{matrix}&1)-z=-(2+i)=-2-i;\quad 2)-z=-(1-5i)=-1+5i;\\&3)-z=-(-2+18i)=-2-18i;\quad 4)-z=-(-3-i)=3+i\end{matrix}\)

Opposite Fill in the Blanks

The opposite of the number \(z=-4i\) is

Q: \(-z=\)[...]
A: 4i
Feedback (0 to 100%): Solution: \(z=-4i \Rightarrow -z = -(-4i) = 4i\)

Opposite Fill in the Blanks

The opposite of the number \(z=7\) is

Q: \(-z=\)[...]
A: -7
Feedback (0 to 100%): Solution: \(z=7 \Rightarrow -z = -7\)

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Practice