Question

which point shows the location of $z = -3 + 2i$ on the complex plane?
○ c
○ b
○ a
○ d
question 20
given: $z = 3 - 6i$, find $|z|$
○ $3\sqrt{5}$
○ $2\sqrt{5}$
○ $5\sqrt{2}$
○ $4\sqrt{3}$

Explanation:

First Question (Locating $z=-3+2i$)

Step1: Identify real/imaginary parts

For $z=a+bi$, $a=-3$, $b=2$

Step2: Map to complex plane

Plot point $(-3, 2)$; this matches point C.

Step1: Recall modulus formula

For $z=a+bi$, $|z|=\sqrt{a^2+b^2}$

Step2: Substitute $a=3, b=-6$

$|z|=\sqrt{3^2+(-6)^2}=\sqrt{9+36}$

Step3: Simplify the expression

$\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$

Answer:

C

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Second Question (Find $|z|$ for $z=3-6i$)