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Worked solution

Complete the real and imaginary parts table

Complete the real and imaginary parts for the source examples. The first row is already given.

zRe(z)Im(z)
2−3i2-3i22−3-3
5i5i??
44??
00??

CJC · Lecture · Opening activity

Answer

zRe(z)Im(z)
2−3i2-3i22−3-3
5i5i0055
444400
000000

Compare your reasoning

Write each value as z=x+iyz=x+iy, with real x and y. Then Re⁡(z)=x\operatorname{Re}(z)=x and Im⁡(z)=y\operatorname{Im}(z)=y. In particular, 5i=0+5i5i=0+5i, 4=4+0i4=4+0i and 0=0+0i0=0+0i. The Teacher note emphasizes that the imaginary part is the real coefficient y, so it does not contain i: Im⁡(5i)=5\operatorname{Im}(5i)=5, not 5i5i.

How did this question go?

Common mistakes

The imaginary part is the coefficient of i, not the whole imaginary term.